Compressibility Factor:
The ratio of the observed volume of a gas to the calculated volume under given conditions of temperature and pressure is knwon as compressibilty Factor(Z) of the gas. If the observed volume of a gas at pressure $P$ and temperature $T$ is $V_{\text {real }}$ and the calculated volume from ideal gas equation $V_{\text {ideal }}$ is $n R T / P$, then the compressibility factor is $Z=\frac{V_{\text {real }}}{n R T / P}=\frac{P V_{\text {real }}}{n R T} P Z=\frac{V_{\text {real }}}{V_{\text {real }}}$
For an ideal gas, $Z=1$ as $P V=n R T$ and for a real gas $Z^{1} 1$, so the observed volume is either greater or less than the calculated volume. For an ideal gas plot of $Z$ vs. $P$ is a straight line parallel to the pressure axis. As the pressure is varied, Z for real gases deviates from unity.
1. At very low pressures, all gasses have $Z$ close to unity. At low pressures, the volume of gas is large, so the volume of the gas molecules can be neglected and gases can behave as ideal gases.
2. As the pressure increases, the value of $P V / n R T$ first decreases $(Z<1)$, reaches a minimum value and then increases.
3. At high pressures $Z>1$, so the gases become difficult to compress as the pressure increases.
The temperature at which gases show ideal gas behavior for an applicable range of pressure is known as Boyle's temperature or point. It is specific to the nature of the gas. As the temperature increases beyond the Boyle's point, the forces of attraction between gas molecules become weak and gases show positive deviation form $(z>1)$.
Below the Bolye's point, the gases first show a negative deviation from ideality, reach a minimum value with increasing value of pressure and then show positive deviation $(Z>1)$ continuously.
1. The compressibility of a gas is less than unity at S.T.P. Therefore :
(A) $V_{m}>22.4$ litres
(B) $V _{ m }<22.4$ litres
(C) $V_{m}=22.4$ litres
(D) $V_{m}=44.8$ litres
2. Compressibility factor for He behaving as real gas generally is :
(A) 1
(B) $\left(1-\frac{a}{R T V}\right)$
(C) $\left(1+\frac{ Pb }{ RT }\right)$
(D) $\frac{R T V}{(1-a)}$
3. Compressibility factor $( Z )$ for $N _{2}$ at $-23^{\circ} C$ and 820 atm pressure is $1.9$. Find the number of moles of $N _{2}$ gas required to fill a gas cylinder of $95 L$ capacity under the given conditions.
(A) 2000
(B) 200
(C) $2 \times 10^{4}$
(D) Cannot be determined
4. At moderate pressures, the compressibility factor for a particular gas is given by $Z=1+0.34 P-\frac{170 P}{T}$
( $P$ in bar and $T$ in Kelvin). The Boyle's temperature of this gas is
(A) $298 K$
(B) $170 K$
(C) $500 K$
(D) $340 K$
(E) $300 K$
