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Avogadro hypothesis - class-XII

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22.4 litres of a gas at STP weighs 16 g. Identify the gas.

  1. Methane

  2. Carbon monoxide

  3. Ethane

  4. Oxygen


Correct Option: A
Explanation:

At STP,  1 mole of gas occupies $22.4l$.

Given gas occupies $22.4l$ at STP and has weight 16 g.
So molecular weight of gas is 16. 
Thus Ans: Methane (Mol. weight of methane is 16)

All gases have the same number of moles in the same volume at constant temperature and pressure.

  1. Boyle's Law

  2. Charles's Law

  3. Avogadro's Principle

  4. Ideal Gas Law


Correct Option: C
Explanation:

According to the Avogadro's principal, every gas have the same number of moles in the same volume at constant temperature and pressure.

What is the volume of $3.0\times {10}^{20}$ molecules of $HCl (g)$?

  1. $11.2L$

  2. $0.0224L$

  3. $0.0112L$

  4. $22.4L$


Correct Option: C
Explanation:

$1 \space Mole$ of gas at STP occupy $22.4 \space Litres$ of gas

As, $1 \space Mole = 6.02 \times 10^{23}$ molecules $\Rightarrow 22.4 Litres$ 
$3.0 \times 10^{20}$ molecules $\Rightarrow (X)$ 
$\Rightarrow X = \dfrac{22.4 \times 3 \times 10^{20}}{6.02 \times 10^{23}} = 0.0112\space L$

All gases have the same number of moles in the same volume at constant T and P is stated by :

  1. Boyle's law

  2. Charle's law

  3. Avogardro's law

  4. ideal gas law

  5. Dalton's law


Correct Option: C
Explanation:

Avogadro's law states that, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules". For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.

Which statement is linked with the idea that two identical containers filled with different gases will contain the same number of particles?

  1. Mosely

  2. Avagadro

  3. Dalton

  4. Mendeleev


Correct Option: B
Explanation:

Avagadro stated that when two identical containers are filled with different gases at same pressure and temperature, they contain same number of particles.

So, the statement is linked with Avagadro.

What is the volume occupied by 17.75 g of $Cl _2$ at STP?

  1. $5.6l$

  2. $22.4l$

  3. $11.2l$

  4. $2.8l$


Correct Option: A
Explanation:

In order to solve this problem, we would use the ideal gas law formula PV = nRT 

at STP standard temp and pressure is 1 atm and 273k

we have 

P = 1atm, n = $\dfrac{17.75}{70.90}$ mole = 0.250, R = $0.0821$ $atm*L/mol*K$ , T=$273K$

V = $\dfrac {nRT}{P}$

= $0.250\times 0.0821\times 273$

= $5.6L$

answer is A


Which term describes the mass of $6.022\times { 10 }^{ 23 }$ representative particles?

  1. Molar mass

  2. Avogadro's number

  3. Empirical formula

  4. Molecular formula


Correct Option: A
Explanation:

Molar mass of a compound describes the total mass of $6.023 \times 10^{23}$ atoms or particles of the compound.

Ex: Molar mass of $H _2 = 2\space g$

A sample of ammonia has a mass of $51.1g$. How many molecules are in this sample?

  1. $1.8\times {10}^{23}$ molecules

  2. $3.6\times {10}^{23}$ molecules

  3. $9.1\times {10}^{23}$ molecules

  4. $1.8\times {10}^{24}$ molecules


Correct Option: D
Explanation:
given mass of ammonia is 51.1g
in this number of moles =  $\dfrac{51.1}{17.031}$ = 18
Now in a mole, there are Na molecules, this is known $6.023\times 10^{23}$ 
since 1 mol = $6.023\times 10^{23}$ 

thus,

18 mol = $18\times 6.023\times 10^{23}$  = $1.8\times 10^{24}$

How many moles are present in $6.023\times 10^{22}$ molecules of $CO _2$?

  1. 0.2

  2. 0.01

  3. 0.1

  4. 0.02


Correct Option: C
Explanation:

1 mole of $CO _2$ contains 1 $N _A$ molecules. ( $N _A=6.023\times10^{23}$)

Moles present in given sample are: $6.023\times10^{22}\div N _A=0.1$

Two gases A and B are taken in same volume containers under similar conditions of temperature and pressure. In container A, there are '2N' molecules of gas A. How many number molecules does container B have? 

  1. 2N

  2. 4N

  3. N

  4. 8N


Correct Option: A
Explanation:

Avogadro's law: Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

Thus ans is 2N.

Assertion : 20 gm of argon (atomic mass of Ar $=40)$ occupies volume of $22400\ cm^3$ at STP.
Reason : 20 gm of Neon (atomic mass of $Ne=20$) occupies a volume of $22400\ cm^3$ at STP.

  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

  2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.

  3. Assertion is correct but Reason is incorrect.

  4. Assertion is incorrect but Reason is correct.

  5. Both assertion and reason are incorrect.


Correct Option: D
Explanation:

20 g of argon is 0.5 moles and it occupies $(0.5\times 22400=)11200\ cm^3$ at STP.
20 g of Neon is 1 mole and occupies a volume of $22400\ cm^3$ at STP.

Let 'p' be the initial pressure of a gas. If the volume of a given mass of the gas, at constant temperature, becomes three times, the pressure will be:

  1. 3p

  2. p/3

  3. 9p

  4. p


Correct Option: B
Explanation:

According to Boyle's law,

$P _1V _1=P _2V _2$
$pV _1=P _2.3V _1$
$\Rightarrow P _2=p/3$

According to Avogadro's hypothesis, equal volumes of gases under the same conditions of temperature and pressure will contain:

  1. the same number of molecules

  2. different number of molecules

  3. the same number of molecules only if their molecular masses are equal

  4. the same number of molecules if their densities are equal.


Correct Option: A
Explanation:

According to avogadro's hypothesis, equal volumes of gases under the same conditions of temperature and pressure will contain, the same no. of molecules.

For eg. One volume of hydrogen combines with one volume of chlorine to produce two volumes of HCl gas.
$H _2\1vol$   $+$  $Cl _2=\1 vol$ $2HCl\2 vol$

Which of the following statements is the most accurate with regard to the significance of Avogadro's number, $6.02 \times 10^{23}$ ?

  1. It is the conversion factor between grams and atomic mass units.

  2. It is a universal physical constant just as the speed of light.

  3. It is the number of particles that is required to fill a $1\ L$ container.

  4. It is the inverse diameter of an $H$ atom .


Correct Option: A
Explanation:

A carbon atom weighs 12 AMU, one AMU is equivalent to $1.66 \times 10^{-24}$ grams. Conversely, one gram is equivalent to $6.022 \times 10^{23}$ AMU, which is called Avogadro's number


so the answer is A

The volume occupied by half a mole of a gas at STP is:

  1. 5.6 L

  2. 11.2 L

  3. 22.4 L

  4. 44.8 L


Correct Option: B
Explanation:
The volume occupied by 1 mole of any gas is 22.4 litres.

So the volume occupied by half a mole of gas would be half of 22.4 litres.

So it will be $11.2\ litres$.

Hence, option B is correct.

At constant temperature, in a given mass of an ideal gas:

  1. the ratio of pressure and volume always remains constant

  2. volume always remains constant

  3. pressure always remains constant

  4. the product of pressure and volume always remains constant


Correct Option: D
Explanation:

Boyle's Law states that, at constant temperature, the product of the pressure and volume of a given mass of an ideal gas in a closed system, is always constant.

The critical volume of a gas is 0.036 $lit. mol^{-1}$. The radius of the molecule will be (in cm):
(Avogadro Number = $6 \times 10^{23}$)

  1. $\displaystyle \left( \frac{9}{4 \pi} \times 10^{-23} \right)^{\dfrac{1}{3}}$

  2. $\displaystyle \left( \frac{8 \pi}{3} \times 10^{-23} \right)^{\dfrac{1}{3}}$

  3. $\displaystyle \left( \frac{3}{8 \pi} \times 10^{-23} \right)^{\dfrac{1}{3}}$

  4. none of these


Correct Option: C
Explanation:

Critical volume of gas=3b [for 1 molecule]

For 1 mole, critical volume=0.036 liters
$\Longrightarrow 0.036\times { 10 }^{ 3 }{ cm }^{ 3 }=3\left( \cfrac { 4 }{ 3 } \pi { r }^{ 3 } \right) \times { N } _{ A } \ \Longrightarrow r={ \left( \cfrac { 36 }{ 24\pi  } \times 10^{ -23 } \right)  }^{ \cfrac { 1 }{ 3 }  }={ \left( \cfrac { 3 }{ 8\pi  } \times 10^{ -23 } \right)  }^{ \cfrac { 1 }{ 3 }  }$

The mass of a molecule of the compound $C {60}H _{122}$ is _________.

  1. $1.4\times 10^{-21}$ g

  2. $1.09\times 10^{-21}$ g

  3. $5.025\times 10^{23}$ g

  4. $16.023\times 10^{23}$ g


Correct Option: A
Explanation:

Molecular mass of $C _{60}H _{122}=(60 \times 12+1 \times 122)=720+122=842$


Hence, one mole contains $6.022 \times 10^{23}$ molecules 


Therefore, 

Mass of one molecule $=\frac{842}{6.022 \times 10^{23}}$

$=1.4 \times 10^{-21}\;g$


The correct option is A.

If you are given Avogadro's number of atoms of a gas $X$. If half of the atoms are converted into $X _{(g)}^+$ by energy $\Delta H$. The IE of $X$ is :

  1. $\dfrac{2\Delta H}{N _A}$

  2. $\dfrac{2N _A}{\Delta H}$

  3. $\dfrac{\Delta H}{2N _A}$

  4. $\dfrac{N _A}{\Delta H}$


Correct Option: A
Explanation:
Given no. of atoms = Avogadro's no. of atoms = ${N} _{A} = 6.023 \times {10}^{23}$
Given that $\cfrac{{N} _{A}}{2}$ atoms are ionized, i.e.,
Ionization energy of $\cfrac{{N} _{A}}{2}$ atoms of gas X = $\Delta{H}$

$\therefore$ Ionization energy of 1 atom of gas X = $\cfrac{\Delta{H}}{\left( \cfrac{{N} _{A}}{2} \right)} = \cfrac{2. \Delta{H}}{{N} _{A}}$
Hence, Ionisation energy of gas X is $\cfrac{2. \Delta{H}}{{N} _{A}}$.

Assuming that the all volume is measured at the same temperature and pressure, state the volume ratios of the reactants and products for the following gaseous reactions. Nitrogen reacting with oxygen to form nitrogen (III) oxide.

  1. 1 : 3 : 2

  2. 2 : 4 : 2

  3. 2 : 2: 1

  4. 2 : 3 : 2


Correct Option: D
Explanation:

The equation for the reaction between nitrogen and oxygen to form Nitrogen (lll) oxide is written as:
$2N _{2} + 3O _{2} \rightarrow 2N _{2}O _{3}$
Therefore the volume ratio of reactants and products $= 2 : 3 : 2$

Ethane burning in oxygen to give carbon dioxide and steam. The volume ratio of reactants to products is ______________.

  1. 2 : 6 : 4 : 3

  2. 2 : 7 : 2 : 5

  3. 3 : 4 : 4 : 6

  4. 2 : 7 : 4 : 6


Correct Option: D
Explanation:

The equation for the combustion reaction of ethane can be written as :
$2C _{2}H _{6} + 7O _{2} \rightarrow 4CO _{2} + 6H _{2}O$
Therefore the volume ratio of reactants and products $= 2 : 7 : 4 : 6$

The number of atoms in 67.2 L of ${ NH } _{ 3 }$(g) at STP is:

  1. 9 ${N } _{ A }$

  2. 12 ${N } _{ A }$

  3. 3 ${N } _{ A }$

  4. 4 ${N } _{ A }$


Correct Option: B
Explanation:
By Avogadro law,
 22.4 liter of any gas at STP$ = $1mole
                $ =6.022\times { 1 }0^{ 23 }$ molecules of gas
                $ =$NA (Avogadro number)

So, in 67.2 L of ${ NH } _{ 3 }=?$
    22.4 L of $ { NH } _{ 3 }=N _A$
     1 L of ${ NH } _{ 3 }=\cfrac { NA }{ 22.4 } $

67.2 L of $ { NH } _{ 3 }=\cfrac { 67.2 }{ 22.4 } \times NA$
                          $ =3N _A$ molecules

Now, each molecule contain 4 atoma
Number of atoms $= 4\times 3N _A = 12N _A$ atoms

Four one litre flasks are separately filled with gases $O _2, F _2, CH _4$ and $CO _2$ under same conditions. 


The ratio of the number of molecules in these gases are:

  1. $2 : 2 : 4 : 3$

  2. $1 : 1 : 1 : 1$

  3. $1 : 2 : 3 : 4$

  4. $2 : 2 : 3 : 4$


Correct Option: B
Explanation:
Avogadro's law: It states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

$\\ n _{1} : n _{2} : n _{3} : n _{4} = \cfrac{PV}{RT} : \cfrac{PV}{RT} : \cfrac{PV}{RT} : \cfrac{PV}{RT} = 1 : 1 : 1 : 1 $

So, the ratio of no. of molecules $= 1: 1: 1: 1$

The correct option is $B.$

A sample of municipal water contains one part of urea (molecular wt $=60$) per million parts of water by weight. The number of urea molecules in a drop of water of volume $0.05\ ml$ is 

  1. $2.5\times 10^{14}$

  2. $5\times 10^{14}$

  3. $5\times 10^{13}$

  4. $5\times 10^{15}$


Correct Option: B
Explanation:

$1 \ ppm = 1 \ mg/L = 10^{-3} g/L$

Water sample contains $1 \ ppm$ urea concentration.

$\therefore \ 10^{-3} \ g$ of urea in $ 1 \ L$

$x \ g$ urea in $0.05 \times 10^{-3} \ L$

$x= 0.05 \times 10^{-6} \ g$

$60 \ g$ urea $=6.023 \times 10^{23} \ molecules$

$0.05 \times 10^{-6} \ g = n \ molecules$

$n = \cfrac {6.023 \times 10^{23} \times 0.05 \times 10^{-6}}{60}$

$=0.005 \times 10^{17}$

$=5 \times 10^{14} \ molecules$

According to Avogadro's law the volume of a gas will ____ as _____ if ____ are held constant.

  1. increases, number of moles; P & T

  2. decreases, number of moles; P & T

  3. increases; T & P; number of moles

  4. decreases; P & T; number of moles


Correct Option: A
Explanation:

According to Avogadro's law: Equal volume of all gases at same temperature and pressure will have same no. of molecules.

OR
For a given mass of ideal gas,
Volume$\propto$Number of moles of the gas (if temperature and pressure are constant) 
So, volume of the gas will increase as the number of moles if pressure (P) and temperature (T) are held constant.

What is the value of $n$ in the following equation?


$Cr\left( OH \right) _{ 4 }^{ - }+OH^{ - }\longrightarrow  Cr{ O } _{ 4 }^{ 2- }+H _{ 2 }O\ +\ ne^-$

  1. $3$

  2. $6$

  3. $5$

  4. $2$


Correct Option: B

The critical density of the gas $CO _2$ is 0.44 $g\ cm^{–3}$ at a certain temperature. If $r$ is the radius of the molecule, $r^3$ in $cm^3$ is approximate: 


[N is Avogadro number]

  1. $\cfrac {25} {\pi N}$

  2. $\cfrac {100} {\pi N}$

  3. $\cfrac {6} {\pi N}$

  4. $\cfrac {25} {4N\pi}$


Correct Option: B
Explanation:
Critical density of a gas $= 0.44 gcm^{-3}$
Molar mass of $CO _2$ = 44 g/mole

$Density = mass /volume $
Mass of N molecules = 44 g of $CO _2$    $N =6.022\times 10^{23}$

Mass of 1 molecule $= \dfrac{44}{N}$
The volume of 1 molecule $=\cfrac {4}{3}\pi r^3$
Putting the values,
$ 0.44 = \dfrac{\dfrac{44}{N}}{\cfrac {4}{3}\pi r^3}$

$ r^3 = \dfrac{100}{\pi N}$

Which facts are revealed from Avogadro's law for ideal gases?

  1. The distance between molecules is much large than the actual dimension of molecules.

  2. Equal number of molecules of different gases under identical conditions of temperatures and pressure occupy the same volume.

  3. Saturated vapours obey gas laws

  4. 1 mole of a gas contains $6.023\times 10^{23}$ molecules of gases.


Correct Option: B,D
Explanation:

Avogadro's Law :
It states "equal volumes of any two gases at the same temperature and pressure contain the same number of molecules".

$V  \propto  n$ (At constant P and T)

$\dfrac{V _1}{V _2} = \dfrac{n _1}{n _2}$

and each gas's one mole contains $6.023\times 10^{23}$ molecules.

The law which suggests $n _1 = n _2$ for two solutions at same temperature and pressure is 

  1. van't Haff - avogadro's law

  2. van't Hoff Boyle's law

  3. van't Hoff's law

  4. Henry's law


Correct Option: C

One gram molecule of any gas at $NTP$ occupies $22.4\ L$. This fact was derived from:

  1. Dalton's theory

  2. Avogardro's hypothesis

  3. Berzelius hypothesis

  4. Law of gaseous volume


Correct Option: B
Explanation:

According to Avogadro's law, 1 mole of every gas occupies 22.4L at $NTP$.

From ideal gas equation,
$PV=nRT$. . . . . . .(1)
At $NTP$,
$T=273K$
$P=1atm$
$n=1$
$R=0.0821atm L/K mol$
from equation (1),
$V=\dfrac{nRT}{P}$
$V=\dfrac{1\times 0.0821\times 273}{1}=22.4L$
The correct option is B.

If  $N _ { A }$ is Avogadro's number, then calculate the number of electrons in  $4.2\ g$  of  $N ^ { 3- }$.

  1. $2.1 N _ { A }$

  2. $3 N _ { A }$

  3. $6 N _ { A }$

  4. $ N _ { A }$


Correct Option: A
Explanation:
$N^{3-}$ contains 10 electrons.

Number of moles $= \dfrac {4.2}{14} $
                                     
                                       $=0.3\ moles$

No of electrons in $0.3\ moles = 0.3\times N _A\times 10$

                                        $=3\ N _A$

Hence, option B is correct.

Mass of the one atom of the element X is $1.66 \times 10^{-26}$ g. Number of atoms in 1 g of the element is:

  1. $1.66 \times 10^{-26}$

  2. $1.66 \times 10^{25}$

  3. $1.66 \times 10^{-24} x No$

  4. $6.024 \times 10^{25}$


Correct Option: D
Explanation:

Mass of one atom = $1.66 \times 10^{-26} g$
$1.66 \times 10^{-26} gm \rightarrow 1 \, atom$
$1 \, gm \rightarrow \dfrac{1}{1.66 \times 10^{-26}} $ atom
$= 6.024 \times 10^{25} atom$

Which of the following represents the Avogadro number?

  1. Number of molecule present in 1 L of gas at N.T.P

  2. Number of molecule present in 22.4 L of gas at N.T.P

  3. Number of molecule present in 22.4 of gas at 298K and 1 atm pressure

  4. Number of molecule present in one mole of gas at any temp and pressure


Correct Option: D

A vessel contains N molecules of oxygen at a certain temperature and pressure. How many molecules of sulphur dioxide can the vessel accommodate at the same temperature and pressure.

  1. N

  2. 2N

  3. N/2

  4. 4N


Correct Option: A
Explanation:

As both have same volume and according to avagadro's law, equal volume of gases contains equal molecules so sulphur dioxide contains N molecules.

The gases chlorine, nitrogen, ammonia and sulphur dioxide are collected under the same conditions of temperature and pressure. If 20 litres of nitrogen contains 'x' no. of molecules, state the no. of molecules in 20 litres of ammonia.

  1. x

  2. x/2

  3. x/4

  4. 2x


Correct Option: A
Explanation:

According to avagadro's law, equal volume of gases contains equal number of molecules. Therefore,  20 litres of ammonia will contain x number of molecule. 

A vessel contains X number of molecules of hydrogen gas at a certain temperature and pressure. Under the same conditions of temperature and pressure, how many molecules of nitrogen gas would be present in the same vessel?

  1. 2X

  2. X

  3. 0.5X

  4. 3X


Correct Option: B
Explanation:

Avogadro's law states that, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules" so same volume of nitrogen will have X number of molecules.

Statement: Equal volumes of all gases always contain equal number of moles.

State whether the given statement is true or false.
  1. True

  2. False


Correct Option: A
Explanation:

 Avogadro law: It states that equal volumes of all gases under the same conditions of temperature and pressure contain the equal number of molecules. 

This means that as long as the temperature and pressure remain constant, the volume depends upon number of molecules of the gas.

Since volume of a gas is directly proportional to the number of moles; one mole of each gas at standard temperature and pressure (STP) will have same volume. 

Hence, the given statement is $\text{true}$

If $1$ L of $O _2$ at $15^oC$ and $750$ mm pressure contains $\text N$ molecules, the number of molecules in $2$ L of $SO _2$ under the same conditions of temperature and pressure will be :

  1. $\dfrac {\text N}{2}$

  2. $\text N$

  3. $2\text N$

  4. $4\text N$


Correct Option: C
Explanation:

Under similar conditions of temperature and pressure, equal volume of gas contains equal number of molecules.
$\therefore 1\ L=N$ molecules
$2\ L=2\ N$ molecules

Under the same conditions, two gases have the same number of molecules. They must:

  1. be noble gases

  2. have equal volumes

  3. have a volume of 22.4 dm$^3$ each

  4. have an equal number of atoms


Correct Option: B
Explanation:

Avogadro's hypothesis: Equal volume of all gases have equal number of molecules (not atoms) at same temperature and pressures conditions.

Four 1-1 litre flasks are separately filled with the gases $H _2,\, He,\, O _2$ and ozone. The ratio of total number of atoms of these gases present in different flask would be : 

  1. 1 : 1 : 1 : 1

  2. 1 : 2 : 2 : 3

  3. 2 : 1 : 2 : 3

  4. 3 : 2 : 2 : 1


Correct Option: C
Explanation:

According to Avogadro's law, all gases at same temperature and pressure will contain same number of molecules. Hence, number of molecules of all gases will be same bt ration of atoms of each gases will $2:1:2:3$.

Number of water molecules in one litre of pure water is :

  1. $6.023 \times 10^{23}$

  2. $3.45 \times 10^{25}$

  3. $55.4 \times 10^{23}$

  4. $18 \times 10^{23}$


Correct Option: B
Explanation:

One mole of water has a mass of $18$ grams and a volume of $18$ mL (as the density of water is 1 g per cm$^3$).


Therefore, number of moles of water in $1$ litre $= \dfrac{1\times 1000}{18}$.

Number of molecules $= $ Number of moles $\times N _A$

                                          $= \dfrac{1\times 1000}{18} \times 6.023\times 10^{23}$

                                         $= 3.45\times 10^{25}$ molecules.

Hence, the correct answer is option $\text{B}$.

Statement 1: The number of gram molecules of oxygen in $6.02 \times 10^{24}\ CO$ molecules is 5.0.
Statement 2: The value of Avogadro number is $6.02 \times 10^{23}$

  1. Statement 1 is True, statement 2 is True, Statement 2 is a correct explanation of statement 1.

  2. Statement 1 is True, statement 2 is True, Statement 2 is not a correct explanation of statement 1.

  3. Statement 1 is True, Statement 2 is False.

  4. Statement 1 is False, Statement 2 is True.


Correct Option: B
Explanation:

$6.02\times 10^{24}$ molecules of $CO=6.02\times 10^{23}\times 10$ i.e.., 10 moles of CO.
10 moles of CO contains 10 gm atoms of oxygen i.e.  5 gm molecules of oxygen.
hence the correct answer is A the given assertion is correct and reason is the correct explanation to the assertion.

Avogadro's number is NOT equal to:

  1. the number of atoms in 11.2 L of $\displaystyle { O } _{ 2 }$ at STP

  2. the number of atoms in 1 mole of $\displaystyle He$ at STP

  3. the number of electrons in 96,500 coulombs

  4. the number of $\displaystyle { SO } _{ 4 }^{ 2- }$ ions in 1 L of 0.5 M sulphuric acid


Correct Option: D
Explanation:
$Avogadro's \ Number= N _A= 6.02 \times 10^{23}$
$1$ mole of any substance has $N _A$ number of atoms, molecules or ions etc. 
Therefore, moles of $SO _4^{2-}$ ions in $1 \ L$ of $0.5 \ M \ H _2SO _4$ will be 
$Molarity= \cfrac {Number \ of \ moles}{Volume \ of \ solution \ (in \ L)}$
$0.5 = \cfrac {moles}1$
$Number \ of \ moles = 0.5$
Hence, because $1$ mole of a substance $= N _A$
$\therefore \ 0.5$ moles of $SO _4^{2-} \neq N _A $ (Avogadro Number)

Number of molecules in one litre of water is :

  1. $\displaystyle \frac {6.023}{23.4} \times 10^{23}$

  2. $18 \times 6.023 \times 10^{23}$

  3. $\displaystyle \frac {18}{22.4} \times 10^{23}$

  4. $55.5 \times 6.023 \times 10^{23}$


Correct Option: D
Explanation:

Number of moles of water molecules in 1 litre of water = 55.5 moles

Hence, number of molecules of water = 55.5$\times$ Avogadro number
So, option D is correct.

64 g of sulphur dioxide occupies $22.4\ L$ volume at STP.

  1. True

  2. False


Correct Option: A
Explanation:

Molecular mass of $SO _2$ is 64. 

So, 1 mole (64 grams) of sulphur dioxide will occupy $22.4\ L$ at STP. ( Avogadro's law)

Which of the following expressions is equal to the number of iron ($Fe$) atoms present in $10.0$ g $\displaystyle Fe$ ? (atomic mass of $\displaystyle Fe$ = $55.9$ amu) 

  1. $ 10\times 55.9\times( 6.022\times { 10 }^{ 23 }) $ atoms

  2. $\dfrac{( 6.022\times { 10 }^{ 23 })}{10}\times 55.9$ atoms

  3. $ 10\times \dfrac {( 6.022\times { 10 }^{ 23 } )}{ 55.9}$ atoms

  4. $\dfrac {55.9}{10} \times ( 6.022\times { 10 }^{ 23 } ) $

  5. $ \dfrac {10}{ ( 55.9\times 6.022\times { 10 }^{ 23 } )} $ atoms


Correct Option: C
Explanation:

The expression $\displaystyle 10\times \left( 6.022\times { 10 }^{ 23 } \right)/ 55.9$ is equal to the number of iron (Fe) atoms present in 10.0 g Fe.
The atomic mass of Fe is 55.9 g/mol.
The mass of Fe is 10.0 g. Mass is divided with atomic mass to obtain number of moles.
The number of moles of Fe $ =  \dfrac {10.0}{55.9}$ moles.
The number of moles is multiplied with avogadro's number to obtain the number of Fe atoms.
The number of Fe atoms  $ =  \dfrac {10.0}{55.9} \times 6.023 \times 10^{23}$.

14 g of nitrogen contains $3.01 \times 10^{23}$ nitrogen molecules.

  1. True

  2. False


Correct Option: A
Explanation:

1 mole nitrogen contains $6.02\times10^{23}$ nitrogen molecules.

Thus 14 gram nitrogen will contain $14/28.Na=0.5Na=3.01\times10^{23}$ nitrogen molecules. ( Molecular weight of nitrogen is 28)

Mass of $12.044 \times 10^{23}$ atoms of hydrogen is:

  1. $1 g$

  2. $2 g$

  3. $3 g$

  4. $4 g$


Correct Option: B
Explanation:
$\dfrac{mass}{molecular\, weight}=\dfrac{No.\, of\, atoms}{N _{A}}$
$mass=\dfrac{12.044\times 10^{23}}{6.022\times 10^{23}}\times 1$ {Hydrogen molecular weight =$ 1 g/mol$}
$Mass = 2g$

1 g of $^{12}C$ contains $6.022 \times 10^{23}$ atoms of the isotope.

  1. True

  2. False


Correct Option: B
Explanation:

Because according to Avegadro's law,

$1$ mole of $C$ contains $6.022\times { 10 }^{ 23 }$ atoms and $1$ mole of $C$ weighs $12gm$
$\therefore$  $12g$ of $C$ weighs $6.022\times { 10 }^{ 23 }$ atoms

Calculate the number of iron atoms in a piece of iron weighing $2.8 g$. (Atomic mass of iron $=56$)

  1. $30.11\times { 10 }^{ 23 }$ atoms

  2. $3.11\times { 10 }^{ 23 }$ atoms

  3. $3.0115\times { 10 }^{ 22 }$ atoms

  4. $301.1\times { 10 }^{ 23 }$ atoms


Correct Option: C
Explanation:
Given that, weight of iron =2.8 g
Atomic mass= 56
moles of iron$= \dfrac{\text{wt. of iron}}{\text{atomic mass}}=\dfrac{2.8}{56}=0.05\ moles$
1 mole $= 6.022 \times 10^{23}\ atoms$
0.05 moles $= 6.022 \times 0.05 \times 10^{23}\ atoms=3.0115 \times 10^{22}$ atoms
Option C is correct.

The value of the Avogadro constant is:

  1. $6.022 \times 10^{13}$

  2. $6.022 \times 10^{22}$

  3. $6.022 \times 10^{23}$

  4. $6.022 \times 10^{24}$


Correct Option: C
Explanation:

Avogadro constant $=6.022\times { 10 }^{ 23 }$


Avogadro constant is the number of constituent particles, usually atoms or molecules, that are contained in the amount of the substance given by one mole.

Therefore, the option is C.

What is the mass of $6.022\times { 10 }^{ 23 }$ molecules of ${NH} _{3}$?

  1. $45.06g$

  2. $19.06\ g$

  3. $17.04g$

  4. $31.02g$


Correct Option: C
Explanation:

$1\space mole$ of $NH _3$ has $6.023 \times 10^{23}$ molecules of $NH _3$.

So, the mass of $6.023 \times 10^{23}$ molecules of $NH _3$. is the mass of $1\space mole$ of $NH _3$  i.e. molar mass of $NH _3.$ 
Molar mass $= 14.01 + 3(1.01) = 17.04 \space g$

What would be the approximate weight of $1.204\times 10^{24}$ bromine atoms?

  1. 80 grams

  2. 120 grams

  3. 160 grams

  4. 180 grams

  5. 200 grams


Correct Option: C
Explanation:

The atomic weight of bromine is 80.

So, 80-gram bromine contains Na atoms.
So, $1.204\times10^{24}$ bromine atoms will weigh:  $80\div 6.02\times10^{23}\times 1.204\times10^{24}=160\ gram$

How many molecules of water are present in a $0.25\ mole$ of $H _2O$?

  1. $6.0\times{10}^{22}$

  2. $4.5\times 10^{23}$

  3. $1.5\times{10}^{23}$

  4. $18\times 10^{23}$


Correct Option: C
Explanation:

$1\space mole$ of a compound has $6.023\times 10^{23}$ molecules in it.

$\Rightarrow 1\space mole =$$6.023\times 10^{23}$ molecules
$ 0.25\space mole = x$ molecules
$\Rightarrow x = (\dfrac{6.023}{4}) \times 10^{23}$$= 1.5\times 10^{23}$ molecules of water.

How many atoms of hydrogen are present in $7.8\ g$ of $Al{(OH)} _{3}$?

  1. $6.0\times {10}^{22}$

  2. $1.8\times {10}^{23}$

  3. $1.7\times {10}^{23}$

  4. $5.1\times {10}^{22}$


Correct Option: A
Explanation:

Molar mass of $Al(OH) _3 = 27 + 3\times 16 + 3\times 1 = 78\space g$

So, no. of moles of $Al(OH) _3 = \dfrac{7.8}{78} = 0.1\space moles$
$1\space mole$ of $Al(OH) _3$ has $6.023 \times 10^{23}$ atoms.
So, $0.1\space moles$ has $6.023 \times 10^{22}$ atoms.

$2K(s)+2{H} _{2}O(l)\rightarrow 2KOH(aq)+{H} _{2}(g)$
If $3.0$ moles of potassium react with excess water, what volume of hydrogen gas will be produced?

  1. $1.5L$

  2. $22.4L$

  3. $67.2L$

  4. $33.6L$


Correct Option: D
Explanation:

Given, $2K(s) + 2H _2O(l) \rightarrow 2KOH(aq) + H _2 (g)$

$2\space moles$ of Potassium on reaction gives $1 \space mole$ of Hydrogen [ 22.4 at STP]
$2\space moles$ of $K \rightarrow 22.4 \space Litres $ of $H _2$
$2\space moles$ of $K = \dfrac{3\times 22.4}{2} = 33.6 \space Litres$ of $H _2$
So, $33.6\space Litres$ of Hydrogen are produced.

Hydrogen, oxygen and carbon dioxide are taken in containers of $2 l$ volume each. Compare the ratio of the number of molecules of the three gases respectively, under same conditions of temperature and pressure.

  1. 1:8:22

  2. 1:1:1

  3. 1:16:44

  4. 1:8:44


Correct Option: B
Explanation:

Using ideal gas law: PV =nRT

n = $\dfrac{V}{RT}$
here P, R and T= Constant, V = 2l
hence number of moles also equal  
the ration of moles equal to 1:1:1
 answer is B

What is the mass of $6.022\times { 10 }^{ 23 }$ formula units of ${({NH} _{4})} _{2}{SO} _{4}$?

  1. $234.11\ g$

  2. $132.11\ g$

  3. $210.29\ g$

  4. $342.14\ g$


Correct Option: B
Explanation:

$1\space mole$ of $(NH _4) _2SO _4$ has $6.023 \times 10^{23}$ formula units.

So, the mass of $6.023 \times 10^{23}$ formula units of $(NH _4) _2SO _4$. is molar mass of $(NH _4) _2SO _4$

Molar mass of $(NH _4) _2SO _4$ $= 2(14 + 4) + 32 + 4\times 16 = 132 \space g$

A mixture of helium and argon contains 3 moles of $He$ for every 2 moles of $Ar$. The partial pressure of argon in the mixture is

  1. two thirds the total pressure

  2. one third the total pressure

  3. three fifths the total pressure

  4. two fifths the total pressure


Correct Option: D
Explanation:

The partial pressure of any gas is the product of mole fraction and total pressure


$P _{Ar}=\dfrac{2}{2+3}.P _{total}$

The volume of 2.8 g of $CO$ at $27^0C$ and 0.821 atm pressure is:

  1. 1.5 litre

  2. 3 litre

  3. 30 litre

  4. 0.3 litre


Correct Option: B
Explanation:

Molecular mass of $CO$ = 28. 

Moles of $CO$ present $= \dfrac{2.8}{28}$
 
$V=\dfrac{nRT}{P}=\dfrac{\dfrac{2.8}{28}\times0.0821\times300}{0.821}=3\ litres$

At what temperature will both Celsius and Fahrenheit scales read the same value:

  1. 100

  2. 180

  3. 40

  4. -40


Correct Option: D
Explanation:

We know, $\dfrac{F-180}{212-180}=\dfrac{C-273}{373-273}$


$F=C=-40$

So, the correct option is $D$

An isobaric process is associated with:

  1. constant temperature

  2. constant volume

  3. constant pressure

  4. small change in enthalpy


Correct Option: C
Explanation:

Isobaric process refers to a process taking place at constant pressure.

What could be better than a dozen $(12)$ donuts? How about a baker's dozen $(13)$ of donuts? Another large unit of measurement is known as Avogadro's number $(6.022\times 10^{23})$.
What is TRUE about Avogadro's number?

  1. Avogadro's number is the number of particles in one mole of any element.

  2. The molar mass of a substance will contain $6.022\times 10^{23}$ molecules.

  3. There are $6.022\times 10^{23}g$ of carbon in $12$ mol of $C - 12$.

  4. $6.022\times 10^{23}$ atoms of any element will have the exact same mass regardless of the identity of the element.


Correct Option: A
Explanation:

Avagadro constant i.e. $6.023 \times 10^{23}$ particles is the number of constituent particles, usually atoms or molecules, that are contained in the amount of substance given by $1\space mole$. 

In the ideal gas equation, the unit of universal gas constant R is?

  1. Mole-atm/K

  2. Litre/mole

  3. Litre-atm/mole.K

  4. erg/K


Correct Option: C
Explanation:

In ideal gas equation,


$R=\dfrac{PV}{nT}$ where, 
$P$ is the pressure in 'Atmosphere (atm)'
$V$ is the volume in Litre
$n$ is the number of moles
$T$ is the Temperature in Kelvin (K) 

$ \therefore $Units of $R$= litre.atm/mol.K

A sample of gas has a volume of 0.2 litres measured at 1 atm pressure and $0^oC$. At the same pressure, at $273^oC$, its volume will become:

  1. 0.1 litre

  2. 0.4 litre

  3. 0.8 litre

  4. 0.6 litre


Correct Option: B
Explanation:

According to Charles's law


$\dfrac{V _1}{T _1}=\dfrac{V _2}{T _2}$

$\dfrac{0.2}{273}=\dfrac{V}{546}$

$V=0.4\ litres$

Weight of 22.4 litres of $Cl _2$ gas at STP is:

  1. 17.25 g

  2. 35.5 g

  3. 73 g

  4. None


Correct Option: D
Explanation:

Volume occupied by 1 mole of any gas at STP is 22.4 litres. Therefore, in the question, we are given 1 mole of $Cl _2$ gas, which weigh 71 g.

A gas is initially at $1$ atm pressure. To compress it to $1/4$ th of its initial volume, pressure to be applied is:

  1. $1$ atm

  2. $2$ atm

  3. $4$ atm

  4. $1/4$ atm


Correct Option: C
Explanation:

According to boyle's law,


$P _1V _1=P _2V _2$

$\Rightarrow 1.V=\frac{V}{4}.P _2$

$\Rightarrow P _2=4\ atm$

Hence, the correct option is $C$

One mole of any substance contains $6.022\times 10^{23}$ atoms/molecules. Number of molecules of $H 2SO _4$ present in $100$mL of $0.02$M $H _2SO _4$ solution is _________?

  1. $12.044\times 10^{20}$ molecules

  2. $6.022\times 10^{23}$ molecules

  3. $1\times 10^{23}$ molecules

  4. $12.044\times 10^{23}$ molecules


Correct Option: A
Explanation:

Moles of $H _2SO _4=$ Molarity of $H _2SO _4\times $ Volume of solution $(L)$


$=0.02\times 0.1$


$=2\times 10^{-3}$ moles

No. of $H _2SO _4$ molecules $=2\times 10^{-3}\times 6.022\times 10^{23}=12.044\times 10^{20}$ molecules


Therefore, the correct option is A.

Cations absorb $6.023\times 10^{22}$ electrons for their reduction. How many equivalents of the ion are reduced?

  1. $0.1$

  2. $0.01$

  3. $0.001$

  4. $0.0001$


Correct Option: A
Explanation:

1 equivalent of ion absorbs 6. 023 $\times 10^{23}$ electrons 

No. of equivalents reduced = $\dfrac{6.023\times 10^{22}}{6.023 \times  10^{23}}$= 0.1

The number of gram molecule of oxygen in $6.02 \times 10^{24}$ CO molecules is :

  1. 10 gm molecules

  2. 5 gm molecules

  3. 1 gm molecules

  4. 0.5 gm molecules


Correct Option: B
Explanation:

Given :


$6.02\times 10^{24}$ $CO$ molecules


We know,

$1$ mole $CO$ equivalent to $6.023\times 10^{23}$ molecules of $CO$

$6.023\times 10^{23}$ molecules of $CO$ contain $6.023\times 10^{23}$ atoms of $O$

Then, $6.02\times 10^{24}$ $CO$ molecules contain $6.02\times 10^{24}$ atoms of $O$

$\Rightarrow$ no. of gram atoms of $O=\cfrac {6.02\times 10^{24}}{6.02\times 10^{23}}$

$=10gm$ atoms  $\longrightarrow 1$

As oxygen is a diatomic molecule.

No. of gm of molecules of oxygen=$\cfrac {10gm\quad atoms}{2\quad atoms/molecule}=5gm$ molecules

Therefore, the correct option is B.

The number of g-atom of oxygen in $6.02\times { 10 }^{ 24 }$ $CO$ molecule is

  1. $1$

  2. $0.5$

  3. $5$

  4. $10$


Correct Option: D
Explanation:

One molecule of $CO$ contains one oxygen atom
$\therefore 6.02\times { 10 }^{ 24 }\quad $ molecules of $CO$ contain $6.02\times { 10 }^{ 24 }$ oxygen atoms
$6.02\times { 10 }^{ 23 }$ atoms of oxygen $\equiv$ $1g$ atom of oxygen
$\therefore 6.02\times { 10 }^{ 24 }$ atoms of oxygen $\equiv$ $10g$ atom of oxygen.

At room temperature and pressure, two flasks of equal volumes are filled with $H _2$ and $SO _2$ separately. Particles which are equal in number, in the two flasks are:

  1. atoms

  2. electrons

  3. molecules

  4. neutrons


Correct Option: C
Explanation:

At a given volume at constant temperature and pressure, two gases have equal no. of moles 

hence, the no. of molecules will be same in both flasks.

Which of the following statement about Avogadro's hypothesis is correct?

  1. Under similar conditions of temperature and pressure, gases react with each other in simple ratio.

  2. Under similar conditions of temperature and pressure, equal volumes of all gases contain same number of molecules

  3. At NTP all gases contain same number of molecules

  4. Gases always react with gases only at the given temperature and pressure


Correct Option: B
Explanation:

Avogadro’s Law states that under same conditions of temperature and pressure, equal volume of all the gases contain equal number of molecules.

The molecular weights of $O _2$ and $N _2$ are $32$ and $28$ respectively. At $15^0$C, the pressure of $1$gm $O _2$ will be the same as that of $1$ gm $N _2$ in the same bottle at the temperature:

  1. $-21^0$C

  2. $-13^0$C

  3. $15^0$C

  4. $56.4^0$V


Correct Option: B
Explanation:
Temperature of $O _{2}$ $=273+15=298 K$

Temperature of $N _{2}$ $=x$

As $n$ $\propto$ $\dfrac 1T$, as pressure is constant.

$\Longrightarrow { n } _{ 1 }{ T } _{ 1 }={ n } _{ 2 }{ T } _{ 2 }\Longrightarrow \left( \cfrac { 1 }{ 32 }  \right) \left( 298 \right) =\left( \cfrac { 1 }{ 28 }  \right) \left( x \right) \\ \Longrightarrow x=\cfrac { 28 }{ 32 } \times 298=260.75K$

Temperature in $^oC=260.75-273=-13 ^oC$

Hence, option $B$ is correct.

When 4 l of nitrogen completely reacts with hydrogen, what would be the volume of ammonia gas formed?

  1. 2 l

  2. 4 l

  3. 5 l

  4. 8 l


Correct Option: D
Explanation:

Reaction:
$N _2+3H _2  \rightarrow 2NH _3$
 1     3               2
so 4 litre of nitrogen will produce 8 litre of $NH _3$

Gram molar volume for a gas is always considered at ___ conditions.

  1. NTP

  2. STP

  3. variable temperature

  4. none of these


Correct Option: B
Explanation:

Since volume is a dependent variable and it depends on pressure and temperature always so temperature and pressure should be specified when volume of gas is considered. For this certain standard conditions are taken as 273 K and 1 atm pressure.
And at STP, molar volume is 22.4 litre.

Two gases A and B are taken in same volume containers under similar conditions of temperature and pressure. In container A, there are '2N' molecules of gas A. The number molecules does container B have :

  1. N

  2. 0.5N

  3. 2N

  4. 4N


Correct Option: C
Explanation:
1. According to Avogadro's law, the equal volume of gases under a similar condition of pressure and temperature contain equal no. of molecules. 
Therefore the number of molecules in container B will also be 2N.

2. As we know, one mole of each gas occupies 22.4-litre volume and one mole of gas contains NA molecules at STP.

So at the same temperature and pressure, the equal volume of gas contains equal no of molecules.

Therefore the number of molecules in container B will also be 2N.

Therefore, the option is C.

Which scientist discovered that the same amount of space was occupied by equal numbers of molecules of gases, irrespective of whether it was hydrogen or chlorine or fluorine?

  1. Gay-Lussac

  2. Avogadro

  3. Marconi

  4. Wohler


Correct Option: B
Explanation:

Avogadro first discovered it.
It states that $1$ $mole$ of any element or compound have $6.022\times 10^{23}$ atoms or molecules present at any constant temperature and pressure.

When a certain quantity of oxygen was ozonised in suitable apparatus, the volume decreased by $4\ ml$. On addition of turpentine the volume further decreased by $8\ ml$. All volumes were measured at the same temperature and pressure. From these data, establish the formula of ozone.

  1. $\displaystyle :O _{3}$

  2. $\displaystyle :O _{4}$

  3. $\displaystyle :O _{5}$

  4. $\displaystyle :O _{6.5}$


Correct Option: A
Explanation:

Let the formula of ozone be $\displaystyle O _n $
When a certain quantity of oxygen was ozonised in suitable apparatus, the volume decreased by 4 ml.
$\displaystyle  nO _2 \rightleftharpoons 2O _n $
$\displaystyle n-2 \propto 4 $
On addition of turpentine the volume further decreased by 8ml. All volumes were measured at the same temperature and pressure.
$\displaystyle  8mL = 2\times 4mL $
$\displaystyle 2=2n-4 $
$\displaystyle 6=2n $
$\displaystyle  n=3$
Thus, the formula of ozone is $\displaystyle O _3 $.

Two gases A and B which react according to the equation $\displaystyle :aA _{(g)}+bB _{(g)}\rightarrow cC _{(g)}+dD _{(g)}$ to give two gases C and D are taken (amount not known) in an Eudiometer tube (operating at a constant pressure and temperature) to cause the above. If on causing the reaction there is no volume change observed then which of the following statement are correct :

  1. $\displaystyle :\left ( a+b \right)= \left ( c+d \right )$

  2. Average molecular mass may increase or decrease if either of A or B is present in limited amount.

  3. Vapour Density of the mixture will remain same throughout the course of reaction.

  4. Total moles of all the component of mixture will change.


Correct Option: A,C

Statement 1: At the same temperature and pressure, 1 L of hydrogen gas and  1 L of neon gas have the same mass.
Statement 2:
Equal volumes of ideal gases at the same temperature and pressure contain the same number of moles.

  1. Both statement 1 and statement 2 are correct and statement 2 is the correct explanation of statement 1

  2. Both statement 1 and statement 2 are correct but Statement 2 is not the correct explanation of Statement 1

  3. Statement 1 is correct but statement 2 is incorrect

  4. Statement 1 is incorrect but statement 2 is correct

  5. Both the statement 1 and statement 2 are incorrect


Correct Option: D
Explanation:

Statement 1: At the same temperature and pressure, 1 L of hydrogen gas and  1 L of neon gas have the same volume.
Statement 2: Equal volumes of ideal gases at the same temperature and pressure contain the same number of moles.
For example, 1 mole of any gas at STP will occupy a volume of 22.4 L.
Hence, statement 1 is not correct but statement 2 is correct.

"All gases have the same number of moles in the same volume at constant temperature and pressure:. This statments belongs to :

  1. Boyle's law

  2. Charles's law

  3. Avogadro's principle

  4. ideal gas law

  5. Dalton's law


Correct Option: C
Explanation:

Avogadro's law (sometimes referred to as Avogadro's hypothesis or Avogadro's principle) is an experimental gas law relating volume of a gas to the amount of substance of gas present.
Avogadro's law states that, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules".
For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.

Avogadro's law shows the relationship between which two variables?

  1. Volume and number of moles

  2. Pressure and number of moles

  3. Volume and pressure

  4. Temperature and pressure

  5. Temperature and number of moles


Correct Option: A
Explanation:

(A) : Volume and number of moles, : at constant pressure.
Avogadro Law: At the same condition of temperature and pressure the volume of the gas is directly proportional to the number of the moles.

Statement I : At STP, 22.4 liters of He will have the same volume as one mole of $\displaystyle { H } _{ 2 }$ (assume ideal gases).
Statement II : One mole or 22.4 liters of any gas at STP will have the same mass.

  1. true, false

  2. false, true

  3. true, true, correct explanation

  4. true, true, not correct explanation


Correct Option: A
Explanation:

Avogadro’s law states that under the same conditions of temperature and pressure, equal volumes of different gases contain an equal number of molecules. This empirical relation can be derived from the kinetic theory of gases under the assumption of a perfect (ideal) gas. The law is approximately valid for real gases at sufficiently low pressures and high temperatures.
At STP, all gas have same volume for 1 mol of gas and that volume is always equal to the 22.4 L.  

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