A sealed vessel of volume 2.0 L contains 8.34 g of PCl5 (molar mass 208.5 g/mol) which dissociates by PCl5(g) PCl3(g) + Cl2(g). The vapour density of the equilibrium mixture is 80. K_c (in mol/L) is

JEE Advanced levelSingle correct optionDifficulty 3 of 3ce199

A sealed vessel of volume $2.0 L$ contains $8.34 g$ of $PCl X_{5}$ (molar mass $208.5 g/mol$ ) which dissociates by $PCl X_{5} (g) PCl X_{3} (g) + Cl X_{2} (g)$ . The vapour density of the equilibrium mixture is $80$ . $K_{c}$ (in mol/L) is

n_{0} = 8.34/208.5 = 0.040

mol.

α = (104.25 - 80) /80 = 0.3031

K_{c} = \frac{α ^{2} n _{0}}{V ( 1 - α )} = \frac{( 0.3031 ) ^{2} \times 0.040}{2.0 \times 0.6969} = 0.0026

mol/L. Omitting

n_{0} / V

or using a wrong

α

gives the other values.