Identify the correct statements from the following I. For an ideal gas, the compressibility factor is 1.0 II…
Identify the correct statements from the following
I. For an ideal gas, the compressibility factor is 1.0
II. The kinetic energy of NO (g) (molar mass $=30 \mathrm{~g}$ $\mathrm{mol}^{-1}$ ) at $\mathrm{T}(\mathrm{K})$ is $x \mathrm{~J} \mathrm{~mol}^{-1}$. The kinetic energy of $\mathrm{N}_2 \mathrm{O}_4(\mathrm{~g})$ (molar mass $\left.=92 \mathrm{~g} \mathrm{~mol}^{-1}\right)$ at $\mathrm{T}(\mathrm{K})$ is $2 x \mathrm{~J} \mathrm{~mol}^{-1}$
III. The rate of diffusion of a gas is inversely proportional to square root of its density
I, II, III
II, III only
I, III only
I, II only
Solution
(I) Compressibility factor (z), is the ratio of PV and nRT.
Mathematically, $Z=\frac{P V}{n R T}$
$\mathrm{Z}=1$ at all temperatures and pressures, for an ideal gas, because for a ideal gas.
$\mathrm{pV}=\mathrm{nRT}$
(II) For one mole of an ideal gas
$K \cdot E=\frac{3}{2} R T$
$\therefore$ Kinetic energy is directly proportional to the absolute temperature, it is independent of the mass of the gas.
Hence, Statement (II) is incorrect.
(III)According to Graham's law of diffusion rate of diffusion (r) is inversely proportional to the square root of density.
Hence, Statement (III) is correct.