Optimizing the Design Solution - Criteria may need to be broken down into simpler ones that can be approached systematically, and decisions about the priority of certain criteria over others (tradeoffs) may be needed.

When $3.06\mathrm{g}$ of solid ${\mathrm{NH}}_4\mathrm{HS}$ is introduced into a two litre evacuated flask at  $27°\mathrm{C},30\mathrm{\%}$ of the solid decomposes into gaseous ammonia and hydrogen sulphide.

The values of  ${\mathrm{K}}_{\mathrm{c}}$  and  ${\mathrm{K}}_{\mathrm{p}}$  for the reaction at $\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}27°C$  would be:

At constant temperature, the equilibrium constant  $\left({\mathrm{K}}_{\mathrm{p}}\right)$ for the decomposition reaction  ${\mathrm{N}}_2{\mathrm{O}}_4\left(\text{g}\right)\rightleftharpoons 2{\mathrm{NO}}_2\left(\text{g}\right)$  is expressed by ${\mathrm{K}}_{\mathrm{p}}=\frac{4{\mathrm{x}}^2}{1-{\mathrm{x}}^2}\mathrm{P}$ , where P = pressure, $\mathrm{x}$ = extent of decomposition. Which one of the following statements is true?

At constant temperature, the equilibrium constant  $\left(K_p\right)$ for the decomposition reaction  ${\mathrm{N}}_2{\mathrm{O}}_4\left(\text{g}\right)\rightleftharpoons 2{\mathrm{NO}}_2\left(\text{g}\right)$  is expressed by ${\mathrm{k}}_{\mathrm{p}}=\frac{\left(4{\mathrm{x}}^2\mathrm{P}\right)}{(1-{\mathrm{x}}^2)}$ , where P = pressure, x = extent of decomposition. Which one of the following statements is true?

For the reversible reaction,  ${\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{NH}}_3\left(\mathrm{g}\right)$ at $500°\mathrm{C}$, the value of  ${\mathrm{K}}_{\text{p}}$ is  $1.44\times {10}^{-5}$ when partial pressure is measured in the atmosphere. The corresponding value of  ${\mathrm{K}}_{\text{c}}$, with concentration in $\mathrm{mol} {\mathrm{L}}^{-1}$, is: 

For the reversible reaction ${\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\text{g}\right)\rightleftharpoons 2{\mathrm{NH}}_3\left(\mathrm{g}\right)$ at $\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}500°C$, the value of ${\mathrm{K}}_{\text{p}}$ is $1.44\times {10}^{-5}$ when partial pressure is measured in atmosphere. The corresponding value of ${\mathrm{K}}_{\text{c}}$, with concentration in $\mathrm{mol} {\mathrm{litre}}^{-1}$, is:

When 3.06 g of solid  ${\text{NH}}_4\text{H}\text{S}$  is introduced into a two litre evacuated flask at  $\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}27°\text{C},30\text{\%}$ of the solid decomposes into gaseous ammonia and hydrogen sulphide.

The values of  ${\text{K}}_{\text{c}}$  and  ${\text{K}}_{\text{p}}$  for the reaction at $\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}27°\text{C}$  respectively will be:

For the reversible reaction,  $N_2\left(g\right)+3H_2(\text{g})\rightleftharpoons 2N{H}_3\left(g\right)$ at $\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}500°C$ , the value of  $K_{\text{p}}$ is  $1.44\times {10}^{-5}$ when partial pressure is measured in atmosphere. The corresponding value of  $K_{\text{c}}$ , with concentration in mole ${\mathrm{litre}}^{-1}$ , is –

For the reversible reaction, ${\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\text{g}\right)\rightleftharpoons 2{\mathrm{NH}}_3\left(\mathrm{g}\right)$ at $500°\mathrm{C}$ , the value of ${\mathrm{K}}_{\text{p}}$ is $1.44\times {10}^{-5}$, when partial pressure is measured in the atmosphere. The corresponding value of ${\mathrm{K}}_{\text{c}}$, with the concentration in $\mathrm{mole} {\mathrm{litre}}^{-1}$, is

For the reversible reaction,  ${\text{N}}_2\left(\text{g}\right)+3{\text{H}}_2(\text{g})\rightleftharpoons 2\text{N}{\text{H}}_3\left(\text{g}\right)$ at $\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}500°\text{C}$ , the value of  ${\text{K}}_{\text{p}}$ is  $1.44\times {10}^{-5}$ when partial pressure is measured in atmosphere. The corresponding value of  ${\text{K}}_{\text{c}}$ , with concentration in mole ${\text{litre}}^{-1}$ , is –

For the chemical reaction  $\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}3X\left(g\right)+\text{Y(g)}\rightleftharpoons X_{3}Y\left(g\right)$ , the amount of  $X_{3}Y$ at equilibrium is affected by –

Physical state of reaction & products For the reaction,  ${\text{CO(g) + Cl}}_{\text{2}}\text{(g) }\underset{}{\rightleftharpoons }{\text{ COCl}}_{\text{2}}\text{(g), the }\frac{K_p}{K_c}\text{ is equal to}$ –

For the reaction equilibrium,  ${\text{N}}_{\text{2}}{\text{O}}_{\text{4}}\text{(g) }\underset{}{\rightleftharpoons }{\text{ 2NO}}_{\text{2}}\text{(g)}$ the concentrations of  ${\text{N}}_{\text{2}}{\text{O}}_{\text{4}}$ and  ${\text{NO}}_2$ at equilibrium are  $4.8\times 10^{-2}and1.2\times 10^{-2}mol{L}^{-1}$ respectively. The value of K_c for the reaction is –

Phosphorus pentachloride dissociates as follows, in a closed reaction vessel,  ${\text{PCl}}_{\text{5}}\text{(g) }\underset{}{\rightleftharpoons }{\text{ PCl}}_{\text{3}}{\text{(g) + Cl}}_{\text{2}}\text{(g)}$

If total pressure at equilibrium of the reaction mixture is P and degree of dissociation of  ${\text{PCl}}_{\text{5}}$ is $\mathrm{x}$, the partial pressure of  ${\text{PCl}}_{\text{3}}$ will be :

For the reaction

 $\begin{array}{l}2{\mathrm{NO}}_2\left(\mathrm{g}\right)\underset{}{\rightleftharpoons }2\mathrm{NO}\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\\ ({\mathrm{K}}_{\mathrm{c}}=1.8\times {10}^{-6} \mathrm{at} 184°\mathrm{C})\\ (\mathrm{R}=0.0831 \mathrm{kJ}/(\mathrm{mol}.\mathrm{K}\left)\right)\end{array}$

When  ${\mathrm{K}}_{\mathrm{p}}$ and  ${\mathrm{K}}_{\mathrm{c}}$ are compared at  $\text{184}°\text{C}$ it is found that –

In which of the following equilibrium, change in the volume of the system does not alter the number of moles –