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Standard XII

Chemistry

Van der Waal's Equation

In certain lo...

Question

In certain low pressure region for $1 mol$ of real gas curve of $Z v / s \frac{1}{v}$ is plotted at constant temperature as follows -

then temperature (T) of above mentioned real gas is -
$[Given : a = 5.5 {atm L}^{2} {mol}^{- 2}, R = 0.08 atm L {mol}^{- 1} K^{- 1}$ ]

230.4 K

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312.5 K

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273.15 K

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300 K

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Solution

The correct option is B $312.5 K$
vander Waals equation for low pressure is represented as-
$(P + \frac{a}{V^{2}}) (V) = R T$
$\Rightarrow P V + \frac{a}{V} = R T$
$\Rightarrow Z = 1 - \frac{a}{V R T}$
$Slope = \frac{a}{R T} = 0.22$
$\Rightarrow \frac{5.5}{0.08 T} = 0.22$
$\Rightarrow T = \frac{5.5}{0.08 \times 0.22}$
$\Rightarrow T = 312.5 K$

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Similar questions

Q. The sketch shows the plot of Z v/s P for a hypothetical gas for one mole at three distinct temperature . Boyle's temperature is the temperature at which a gas shows ideal behavior over a pressure range in the low-pressure region .Boyle's temperature

(T_{b})

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Which of the following is correct?

The sketch shows the plot of

Z

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for a hypothetical gas for one mole at three distinct temperature. Boyle's temperature is the temperature at which a gas shows ideal behavior over a pressure range in the low-pressure region. Boyle's temperature

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C O_{2}

and the temperature well above critical temperature curve is more like

H_{2}

O^{o} C

as shown above.At high pressure suppose all the constant temperature curve varies linearly with pressure according to the following equation

Z = 1 + \frac{P b}{R T} (R = 2 c a l m o l^{- 1} K^{- 1}

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For 500

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plot value of

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changes from 2 to 2.2 ,if pressure is varied from 1000

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to 1200

a t m

(high pressure) then the value of

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Q. The graph of compressibility factor

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N_{A} = 6 \times 10^{23}

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In certain low pressure region for 1 mol of real gas curve of Zv/s1v is plotted at constant temperature as follows - then temperature (T) of above mentioned real gas is - [Given:a=5.5 atm L2mol−2,R=0.08 atm L mol−1K−1]

The correct option is B 312.5 K vander Waals equation for low pressure is represented as- (P+aV2)(V)=RT ⇒PV+aV=RT ⇒Z=1−aVRT Slope=aRT=0.22 ⇒5.50.08T=0.22 ⇒T=5.50.08×0.22 ⇒T=312.5 K

In certain low pressure region for $1 mol$ of real gas curve of $Z v / s \frac{1}{v}$ is plotted at constant temperature as follows -

then temperature (T) of above mentioned real gas is -
$[Given : a = 5.5 {atm L}^{2} {mol}^{- 2}, R = 0.08 atm L {mol}^{- 1} K^{- 1}$ ]