Solid ammonium carbamate dissociates according to the given reaction
$N{H_2}COON{H_4}(s) \rightleftharpoons 2N{H_3}(g) + C{O_2}(g)$
a) $18.5$
b) $25$
c) $1/5$
d) $12.5$

Hint: Ammonium carbamate is an organic compound which consists of ammonium and carbamate groups.It appears as a white solid which is extremely soluble in water but less soluble in alcohol. Ammonium carbamate is formed by the reaction of ammonia with carbon dioxide, and will slowly decompose to those gases at ordinary temperatures and pressures. It is often used as an intermediary in the industrial synthesis of urea which is an important fertilizer.

Complete answer:
When the rate of forward reaction equals the rate of backward reaction we say that the reaction is in a state of equilibrium.Although it may look like there is no reaction happening it is quite the opposite since it’s not visible to the naked eye.
The equation proceeds in equilibrium as,
$N{H_2}COON{H_4}(s) \rightleftharpoons 2N{H_3}(g) + C{O_2}(g)$
It’s given that total pressure of gases in equilibrium is,
${P_t} = 5$ $atm$
We know that,
${K_p} = {[{P_{N{H_3}}}]^2}.{P_{C{O_2}}}$ …………………….(1)
Let this be equation number 1
By using Dalton’s law of partial pressure,
${P_i} = {\chi _i}.{P_t}$ …………………..(2)
For ammonia,
${P_{N{H_3}}} = {\chi _{N{H_3}}}.{P_t}$
Calculating ${\chi _{N{H_3}}}$ for ammonia
${\chi _{N{H_3}}} = \dfrac{{{n_{N{H_3}}}}}{{{n_{N{H_3}}} + {n_{C{O_2}}}}} = \dfrac{2}{{2 + 1}} = \dfrac{2}{3}$
Similarly for carbon dioxide,
${\chi _{C{O_2}}} = \dfrac{{{n_{C{O_2}}}}}{{{n_{N{H_3}}} + {n_{C{O_2}}}}} = \dfrac{1}{{1 + 2}} = \dfrac{1}{3}$
By substituting the values which have been obtained in equation number (1) we get,
${K_p} = {\left( {\dfrac{2}{3} \times 5} \right)^2} \times \left( {\dfrac{1}{3} \times 5} \right)$
Solving this equation further we get,
${K_P} = \dfrac{{500}}{{27}} = 18.52$

Hence the correct option is option (a).

Note:
Since ammonium carbamate is an intermediate in the industrial production of urea it is extensively used in those industries.As a matter of fact a typical industrial plant that makes urea can produce up to 1500 tons a day.Often laboratories also use it as an ammoniating agent.Apart from that it can also be used as an starting reagent for production of salts of other cations.