Ammonium carbamate when heated to 200ºC gives a mixture of NH₃ and CO₂ vapour with a density of 13. What is the degree of dissociation of ammonium carbamate?

Ammonium carbamate is NH₄COONH₂ MW of NH₄COONH₂ (undissociated) = 78

VD of NH₄COONH₂ (undissociated) = 39

VD of equilibium mixture (observed vapour density) = 13

Degree of decomposition,$\mathrm{\alpha }=\frac{\mathrm{D}-\mathrm{d}}{\mathrm{d}(\mathrm{n}-1)}$

D = V.D of undissociated species

d = V.D of equilibrium mixture (observed vapour density)

${\mathrm{NH}}_4{\mathrm{COONH}}_2\left(\mathrm{s}\right)\rightleftharpoons 2{\mathrm{NH}}_3( \mathrm{g})+{\mathrm{CO}}_2( \mathrm{g})$

n = 3

D = 39

d = 13

$$\begin{gathered} \alpha =\frac{D-d}{d(n-1)} \\ \alpha =\frac{39-13}{13(3-1)} \\ \alpha =\frac{26}{26} \\ \alpha =1 \end{gathered}$$