Question

At 1990 K and 1 atm pressure, there are equal number of $Cl_2$ molecules and $Cl$ atoms in the reaction mixture. The value of $K_p$ for the reaction $Cl_2(g) \rightleftharpoons 2Cl(g)$ under the above conditions is $x \times 10^{-1}$. The value of $x$ is __________. (Rounded off to the nearest integer)

Hint:

In gas phase equilibria, Dalton's Law states partial pressure is proportional to the mole fraction. Equal moles means equal partial pressures.

Answer 1

Correct Answer: 5

Step 1: Equal number of molecules and atoms implies equal partial pressures. $P_{Cl_2} = P_{Cl}$.
Step 2: Total pressure $P = P_{Cl_2} + P_{Cl} = 1$ atm.
Step 3: $P_{Cl_2} = 0.5$ atm and $P_{Cl} = 0.5$ atm.
Step 4: $K_p = \frac{(P_{Cl})^2}{P_{Cl_2}} = \frac{(0.5)^2}{0.5} = 0.5$ atm.
Step 5: $0.5 = 5 \times 10^{-1}$. Thus, $x = 5$.