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Compressibili...

Compressibility Factor

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Q. A container (volume V) has an ideal gas at 4 atm and 300 K. This is connected by a tube with another container of volume 2 V, which has a gas at 8 atm and 600 K. What will be final pressure of each container if the temperature is maintained - the container with volume V at 300 K and the 2V one at 600 K?

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Q. Compressibility factor for

C O_{2}

at

400 K

and

71.0 bar

is

0.8697

. Molar volume of

C O_{2}

under these conditions is:

$0.40 L$
$2.24 L$
$22.4 L$
$19.5 L$

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Q. At

27^{\circ} C

, hydrogen is leaked through a tiny hole into a vessel for 20 minutes. Another unknown gas at the same temperature and pressure leaked through the same hole for 20 minute. After the effusion of the gases the mixture exerts a pressure of 9 atm. The hydrogen content of the mixture is 0.7 mole. If the volume of the container is 3 L, what is the molecular mass of the unknown gas (in g)?

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Q. The best vacuum attained so far in a laboratory is

10^{- 10} mm

of

H g

. The number of molecules of gas remaining per

c m^{3}

at

20^{\circ} C

in this vacuum is:

$3.29 \times 10^{4}$ molecules
$3.29 \times 10^{5}$ molecules
$3.29 \times 10^{6}$ molecules
$3.29 \times 10^{7}$ molecules

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Q. There are 10 identical containers of volume V, each of them have an ideal gas at a same temperature T. The first container has a pressure of 1 atm, the second one has a pressure of 2 atm, the third has a pressure of 3 atm and so on. The tenth container has a pressure of 10 atm. If all the 10 containers are connected by thin tubes, then what will be the final pressure (in atm)?

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Q.

The reciprocal of compressibility factor of a real gas in the critical state is ?

$\frac{3}{8}$
$\frac{3}{4}$
$\frac{8}{3}$
$\frac{1}{3}$

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Q. The compressibility factors for 1 mole of real gases at low pressure, high pressure and that of gases of very low molar masses are

Z_{1}, Z_{2}

and

Z_{3}

. These are

$Z_{1} = (1 - \frac{a}{R T V}), Z_{2} = 1, Z_{3} = (1 + \frac{P b}{R T})$
$Z_{1} = (1 - \frac{a}{R T V}), Z_{2} = (1 + \frac{P b}{R T}), Z_{3} = 1$
$Z_{1} = (1 + \frac{P b}{R T}), Z_{2} = (1 - \frac{a}{R T V}), Z_{3} = (1 + \frac{P b}{R T})$
$Z_{1} = (1 - \frac{a}{R T V}), Z_{2} = (1 + \frac{P b}{R T}), Z_{3} = (1 + \frac{P b}{R T})$

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Q. At low pressures (For 1 mole), the van der Waals equation is written as

[p + \frac{a}{V^{2}}] V = R T

The compressibility factor is then equal to:

$(1 - \frac{a}{R T V})$
$(1 - \frac{R T V}{a})$
$(1 + \frac{a}{R T V})$
$(1 + \frac{R T V}{a})$

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Q. An ideal gas obeying kinetic theory of gases can be liquefied if:

Its pressure is more than $P_{c}$ at a temperature less than $T_{c}$
Its temperature is more than critical temperature $T_{c}$
Its pressure is more than critical pressure $P_{c}$
It cannot be liquefied at any value of P and T

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Q. The ideal gas law, although convenient, has limitations. Most gases tend to deviate from ideal behaviour. For 1 mole of gas, plotting a curve of

Z = \frac{P V}{R T}

v/s P gives us an idea of the deviation.

For curve C, find

Z

for 1 l of the gas at a pressure where

b

is negligible and

a = 4.225 a t m l^{2} m o l^{2}

0.95
1.46
0.32
0.83

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Q.

The compressibility factor of an ideal gas is –

$Z e r o$
$1$
$\frac{1}{2}$
$N o n e o f t h e a b o v e$

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Q. For a van der Waal's gas

V_{c} = 3 b, P_{c} = \frac{a}{27 b^{2}}

T_{c} = \frac{8_{a}}{27 b R}

. Numerically the compressibility factor of a van der Waals gas at the critical points is:

$0.375$
$1$
$0.952$
$0.567$

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Q. The sketch shows the plot of Z vs P for 1 mole of a hypothetical gas at three distinct
temperatures:

Boyle's temperature is the temperature at which a gas shows ideal behaviour over a
pressure range in the low pressure region. Boyle's temperature

(T_{b}) = \frac{a}{R b}

. If a plot is
obtained at temperatures well below Boyle's temperature, then the curve will show a negative deviation in the low pressure region and a positive deviation in the high pressure
region.

Which of the following is correct?

$\frac{a}{b} < 0.4 k c a l m o l^{- 1}$
$1 k c a l m o l^{- 1} < \frac{1}{2} < 2 k c a l m o l^{- 1}$
$\frac{a}{b} < 0.2 k c a l m o l^{- 1}$
$\frac{a}{b} = 1 k c a l m o l^{- 1}$

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Q. The vapour density of a mixture of

N O_{2}

and

N_{2} O_{4}

at

27^{\circ} C

is 38.3. How many moles of

N O_{2}

will be present in

500 g

of the mixture?

$3.485 mol$
$8.125 mol$
$2.185 mol$
$1.825 mol$

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Q. The number of moles of oxygen in one litre of air containing 21% oxygen by volume under standard conditions is

^{'} X^{'}

. What is the value of

X

?

0.009
9
21
0.21

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Q. The compressibility factor for

H_{2}

which behaves as a real gas is

$1 - \frac{a}{R T V}$
$1 + \frac{P b}{R T}$
$\frac{R T V}{1 - a}$

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Q. The ideal gas law, although convenient, has limitations. Most gases tend to deviate from ideal behaviour. For 1 mole of gas, plotting a curve of

Z = \frac{P V}{R T}

v/s P gives us an idea of the deviation.

For curve C, find

Z

for 1 l of the gas at a pressure where

b

is negligible and

a = 4.225 a t m l^{2} m o l^{2}

0.95
0.32
0.83
1.46

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Q. The equation of state of a gas is

P (V - n b) = n R T

, where

b

and

R

are constants. If the pressure and the temperature are such that

V_{m} = 10 b,

what is the value of compressibility factor?

$\frac{10}{9}$
$\frac{9}{11}$
$\frac{11}{10}$
$\frac{10}{11}$

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Q.

Consider isotherms I, II and III in the figure.

Select the correct statement.

For light gases (like $H_{2}$ ), isotherm I is obtained.
When force of attraction is negligible, isotherms II and III are followed after point B or C .
When co-volume is neglected, isotherms II and III are followed A to B or A to C .
All the statements are correct.

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Q.

What is the compressibility factor for $H_{2}$ which behaves as a real gas?

1
$1 - \frac{a}{R T V}$
$1 + \frac{P b}{R T}$
$\frac{R T V}{1 - a}$

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Q. Assertion (A): At constant temperature,

P V

vs

P

plot for real gases is not a straight line.
Reason (R): At high pressure all gases have

Z > 1

but at intermediate pressure most gases have

Z < 1

.

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is not the correct explanation of A
A is true but R is false
A is false but R is true

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Q. The ideal gas law, although convenient, has limitations. Most gases tend to deviate from ideal behaviour. For 1 mole of gas, plotting a curve of

Z = \frac{P V}{R T}

v/s P gives us an idea of the deviation.

Curve C could be ____.

$H e$ at 650 K
$C O_{2}$ at 20 K
$N H_{3}$ at 300 K
$N_{2}$ at 473 K

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Q.

The compressibility factor for a real gas at high pressure is

$1 + \frac{R T}{p b}$
$1$
$1 + \frac{p b}{R T}$
$1 - \frac{p b}{R T}$

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Q.

The given graph in Fig represents the variation of Z $(c o m p r e s s i b i l i t y f a c t o r = \frac{p V}{n R T}$ ) vs.P , for the three real gases A, B and C.identify the only incorrect statement
$1 - \frac{p b}{R T}$

For the gas A, a=0 and its dependence on p is linear at all pressures
For the gas B, b=0 and its dependence on p is linear at all pressures.
For the gas C, which is typical real gas which neither a nor b=0.By konowing the minima and the point of intersection with z=1, a and b can be calculated.
At high pressure, the slope is positive for all real gases.

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Q. The curve of pressure volume (PV) against pressure (P) of the gas at a particular temperature is as shown, according to the graph which of the following is /are incorrect (in the low pressure region):

$H_{2}$ and $H e$ show positive deviation from ideal gas equation.
$C O_{2}, C H_{4}$ and $O_{2}$ show negative deviation from ideal gas equation.
$H_{2}$ and $H e$ show negative deviation while $C O_{2}, C H_{4}$ and $O_{2}$ show positive deviation.
$H_{2}$ and He are less compressible than that of an ideal gas while $C O_{2}, C H_{4}$ and $O_{2}$ more compressible than that of ideal gas.

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Q.

The compressibility factor of an ideal gas is equal to

0
1
-1
Not defined

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Q.

The compressibility factor of an ideal gas is equal to

0
1
-1
Not defined

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Q.

What is the compressibility factor for $H_{2}$ which behaves as a real gas?

1
$1 - \frac{a}{R T V}$
$1 + \frac{P b}{R T}$
$\frac{R T V}{1 - a}$

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Q. The compressibility of a gas is less than unity at STP. Therefore, its molar volume is

$V_{m} > 22.4 L$
$V_{m} < 22.4 L$
$V_{m} = 22.4 L$
$V_{m} = 44.8 L$

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Q. A gas at 350 K and 15 bar has molar volume 20 percent smaller than that for an ideal gas under the same conditions. The correct option about the gas and its compressibility factor (Z) is :

 NEET 2019

Z > 1 and repulsive forces are dominant
Z > 1 and attractive forces are dominant
Z< 1 and attractive forces are dominant
Z < 1 and repulsive forces are dominant

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