Question

One mole of a mixture of N2, NO2 and N2O4 has a mean molar mass of 55.4. On heating to a temperature at which all the N2O4 may be presumed to have dissociated : N2O4 $\rightleftharpoons$ 2NO2, the mean molar mass tends to the lower value of 39.6. What is the mole ratio of N2 : NO2 : N2O4 in the original mixture ?

• A. 0.5 : 0.1 : 0.4
• B. 0.6 : 0.1 : 0.3
• C. 0.5 : 0.2 : 0.3
• D. 0.6 : 0.2 : 0.2

Answer 1

Answer: (A)

0.5 : 0.1 : 0.4

Answer 2

(1)

Let mol of N2 = x, mol of NO2 = y, mol of N2O4 = z

Therefore $\frac{28x + 46y + 92z}{1} = 55.4$ ...........(1)

If N2O4 $\longrightarrow$ 2NO2

$\frac{28x + (y + 2z)46}{x + y + z + z} = 39.6$

$\Rightarrow$ $\frac{28x + 46y + 92z}{1 + z} = 39.6$ ...........(2)

By deviding equation (1) by equation (2)

1 + z =$\frac{55.4}{39.6}$ = 1.4

z = 0.4 mol

Given x + y + z = 1 ...........(3)

Put the value of z in eq. (1)

28x + 46y + 92 + 0.4 = 55.4

28x + 46y = 18.6 ...........(4)

By equation (3) & (4)

y = 0.1

$\therefore$x = 0.5 , y = 0.1 , z = 0.4