One mole of N2O4 is kept at a constant total pressure of 1.0 atm and constant temperature where K_p = 0.50 atm for N2O4(g) 2NO2(g). How many moles of an inert gas must be mixed in so that the degree of dissociation of N2O4 becomes 0.40? Give the answer to two decimal places.

JEE Advanced levelNumerical answerDifficulty 3 of 3ce216

One mole of $N X_{2} O X_{4}$ is kept at a constant total pressure of $1.0 atm$ and constant temperature where $K_{p} = 0.50 atm$ for $N X_{2} O X_{4} (g) 2 NO X_{2} (g)$ . How many moles of an inert gas must be mixed in so that the degree of dissociation of $N X_{2} O X_{4}$ becomes $0.40$ ? Give the answer to two decimal places.

Numerical answer type, answer in mol, tolerance 0.02.

With

x

mol inert gas:

N X_{2} O X_{4}

0.60

NO X_{2}

0.80

, total

N = 1.40 + x

K_{p} = (0.80/ N)^{2} P / [(0.60/ N)] = 0.64 P / (0.60 N)

. So

N = 0.64/ (0.60 \times 0.50) = 2.1333

and

x = N - 1.40 = 0.7333

mol, i.e. 0.73.