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At low pressure, van der wall's equation is written as $\left(P+\frac{a}{V^2}\right)V=RT$. The compressibility factor is then equal to:
(1) $\left(1-\frac{a}{RTV}\right)$
(2) $\left(1-\frac{RTV}{a}\right)$
(3) $\left(1+\frac{a}{RTV}\right)$
(4) $\left(1+\frac{RTV}{a}\right)$

Calculate the volume occupied by 16 gram O₂ at 300 K and 8.31 MPa if $\frac{{\mathrm{P}}_{\mathrm{C}}{\mathrm{V}}_{\mathrm{C}}}{{\mathrm{RT}}_{\mathrm{C}}}=3/8$ and$\frac{P_r{V}_r}{T_r}=2.21$ (Give : R=8.314 MPa/K-mol)
(1) 125.31 mL
(2) 124.31 mL
(3) 248..62 mL
(4) None of these

For a real gas (mol. mass = 60) if density at critical point is 0.80 g/cm³ and its $T_C=\frac{4\times {10}^5}{821}K,$ then van der Waal's constant a (in atm L² mol^-2) is
(1) 0.3375
(2) 3.375
(3) 1.68
(4) 0.025

Gas molecules each of mass 10^-26 kg are taken in a container of volume 1 dm³. The root mean square speed of gas molecules is 1 km sec^-1. What is the temperature of gas molecules.
(Given : N_A=6$\times {10}^{23}; R=8 J/mol.K)$
(1) 298 K
(2) 25 K
(3) 241 K
(4) 2500 K

At 273 K temp. and 9 atm pressure, the compressibility for a gas is 0.9. The volume of 1 milli-moles of gas at this temperature and pressure is:
(1) 2.24 litre
(2) 0.020 mL
(3) 2.24 mL
(4) 22.4 mL

If the average velocity of N₂ molecules is 0.3 m/s at 27°C, then the velocity of 0.6 m/s will take place at 
(1) 273 K
(2) 927 K
(3) 1000 K
(4) 1200 K

A certain hydrate has the formula ${\mathrm{MgSO}}_4.$ ${\mathrm{xH}}_2\mathrm{O}$. A quantity of 54.2 g of the compound is heated in an oven to drive off the water. If the water vapour generated exerts a pressure of 24.8 atm in a 2.0 L container at 120$°\mathrm{C}$, the value of x is-
1.  2
2.  5
3.  6
4.  7

If the intermolecular forces vanish away, the volume occupied by the molecules of 4.5 kg water at STP will be:
1.  $5.6 {\mathrm{m}}^3$
2.  $4.5 {\mathrm{m}}^3$
3$11.2 {\mathrm{m}}^3$

At sea level air is dense. This is practical application evidence of:
1.  Boyle's law
2.  Charles' law
3.  Dalton's law
4.  Avogadro's law

20 L of ${\mathrm{SO}}_2$ diffuse through a porous partition in 60 s. volume of ${\mathrm{O}}_2$ diffuse under
similar  condition in 30 s will be 
1. 12.14 L 
2. 14.14 L 
3. 18.14 L 
4. 28.14 L