Single Choice

The compressibility factor for a real gas at high pressure is:

A$$1+ \dfrac{RT}{pb}$$
B$$1$$
C$$1+ \dfrac{pb}{RT}$$
Correct Answer
D$$1- \dfrac{pb}{RT}$$

Solution

Real gas equation is $$\displaystyle (P+ \frac{a}{V^2})(V-b)=RT$$
At high pressure, $$\displaystyle \frac{a}{V^2}$$ can be neglected.
$$PV-Pb=RT$$
$$\displaystyle \dfrac{PV}{RT}= 1+ \dfrac{Pb}{RT}$$..........(i)

$$\displaystyle Z= \dfrac{PV}{RT}$$.......(ii)

$$\displaystyle Z=1+\dfrac{Pb}{RT}$$

SIMILAR QUESTIONS

States of Matter - Gas and Liquid

The compressibility factor for $$H_{2}$$ and $$He$$ is usually:

States of Matter - Gas and Liquid

If $$ Z$$ is a compressibility factor, van der Waals equation at low pressure can be written as:

States of Matter - Gas and Liquid

The behaviour of a real gas is usually depicted by plotting compressibility factor Z versus P at a constant temperature. At high temperature and high pressure, Z is usually more than one. This fact can be explained by van der Waal's equation when:

States of Matter - Gas and Liquid

The compressibility factor for $$CO_2$$ at 273 $$K$$ and 100 $$atm$$ pressure is 0.2005. The volume occupied by 0.2 mole of $$CO_2$$ gas at 100 $$atm$$ and 273 $$K$$ using real gas nature is $$8.89\times 10^{-x} \:litre$$. So, value of $$x$$ is.....

States of Matter - Gas and Liquid

At low pressures, the van der Waals equation is written as $$\displaystyle \left [ P+\frac{a}{V^2} \right ]V=RT$$ The compressibility factor is then equal to :

States of Matter - Gas and Liquid

Consider the following table: Gas $$a/(k Pa dm^6 mol^{-1})$$ $$b / (dm^3 mol^{-1})$$ A 642.32 0.05196 B 155.21 0.04136 C 431.91 0.05196 D 155.21 0.4382 a and b are vander waals constant. The correct statement about the gases is:

States of Matter - Gas and Liquid

At very high pressures, the compressibility factor of one mole of a gas is given by :

States of Matter - Gas and Liquid

At a moderate pressure, the van der Waal's equation is written as: $$\left[P+\dfrac{a}{V^2}\right]V=RT$$ The compressibility factor is equal to:

States of Matter - Gas and Liquid

Calculate the number of $$\alpha$$ and $$\beta$$ particles is the following change : $$U^{235}_{92}\longrightarrow \, ^{207}_{82}Pb$$

States of Matter - Gas and Liquid

For a real gas, the compressibility factor $$Z$$ has different values at different temperature and pressures. Which of the following is not correct under the given condition?

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