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Compressibility factor Z of a real gas

This type of question, asked 3 times: 2021 Paper 25, 27 Jul 2022, 13 Apr 2023. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 25

    58
    A certain gas obeys P(Vm−b)=RTP\left( V_{m}-b \right)=RT. The value of (∂Z∂P)T\left( \frac{\partial Z}{\partial P} \right)_{T} is xbRT\frac{xb}{RT}. The value of xx is

  2. Question 2

    27 Jul 2022

    142
    for a real gas at 25∘C25^{\circ}C temperature and high pressure (99(99 bar) the value of compressibility factor is 2, so the value of Vander Waal's constant ' bb ' should be ×10−2 L mol−1\times10^{- 2}\text{ }L{\text{ }mol}^{- 1} (Nearest integer) (Given R=0.083 LR = 0.083\text{ }L bar K   −1 mol−1)\left. \ \ ^{- 1}{\text{ }mol}^{- 1} \right)

  3. Question 3

    13 Apr 2023

    57
    A certain quantity of real gas occupies a volume of 0.15dm30.15dm^{3} at 100 atm100\text{ }atm and 500 K500\text{ }K when its compressibility factor is 1.07. Its volume at 300 atm300\text{ }atm and 300 K300\text{ }K (When its compressibility factor is 1.4) is ×_______10−4dm3\times \_\_\_\_\_\_\_10^{- 4}dm^{3} (Nearest integer)