Question

$CO_{2}$ gas is liquefied at $27^{o}C$ . Gas follows the following graph during liquefaction for 1 mole of $CO_{2}$ .



Then which statement is (are) correct in gaseous phase will

(i) The maximum density of gas is 0.1 gm/ml

(ii) The density of liquid $CO_{2}$ is 1 g/ml at 60 atm.

(iii) At point C 50% of $CO_{2}$ is liquefied.

(iv) The compressibility factor of gas at $27^{o}C$ is always less than 1.

Which of the above is/are correct

• A. only i
• B. i and ii
• C. i,ii and iii
• D. all

Answer 1

Answer: (C)

$\left(A\right)$ Maximum density of $CO_{2}$ in gaseous phase will be at point 'A'

Now: $d=\frac{P M}{R T}=\frac{60 \times 44}{R \times 300}=107 \, g m / l t=0.107 \, g m / c c$

Or $d=\frac{m a s s \, o f \, g a s}{V o l u m e \, o f \, g a s}=\frac{44 \, g m}{440 \, c c}=0.1$

$\left(B\right)$ Density of liquid $CO_{2}$ at 60 atm (at point B)

At point B there will be only liquid $CO_{2}$ . So we can find out the density of density of liquid $CO_{2}$ only at point B.

$\text{d} = \frac{\text{M}}{\text{V}} = \frac{44}{0.044} = 1 \text{ gm/cc}$

$\left(C\right)$ at point C the volume will be $\frac{0.44 + 0.044}{2} \approx 0.22 \, \text{L}$

And pressure is same so obviously approx. half of $CO_{2}$ is liquified

$\left(D\right)$ Z can be greater than 1 at $27^{ο}C$ . For example at point 'A' Z is 1.07, So wrong.