Effective Equilibrium Constant

Q. The equilibrium constants for the following are:
$N_2+3H_2\rightleftharpoons 2N{H}_3{K}_1$
$N_2+O_2\rightleftharpoons 2NO{K}_2$
$H_2+\frac{1}{2}{O}_2\to H_{2}O{K}_3$
The equilibrium constant (K) of the reaction:
$2N{H}_3+\frac{5}{2}{O}_2\stackrel{K}{\rightleftharpoons }2NO+3H_{2}O,$ will be

1. $K_1{K}_3^3/K_2$
2. $K_2{K}_3^3/K_1$
3. $K_2{K}_3/K_1$
4. $K_2^3{K}_3/K_1$

Q.

An aqueous solution contains $0.10\mathrm{M}{\mathrm{H}}_2\mathrm{S}$ and $0.20\mathrm{M}\mathrm{HCl}$. If the equilibrium constants for the formation of ${\mathrm{HS}}^{-}$ ions from ${\mathrm{H}}_2\mathrm{S}$ is $1.0\times {10}^{-7}$ and that of ${\mathrm{S}}^{2-}$ from ${\mathrm{HS}}^{-}$ ions is $1.2\times {10}^{-13}$ then the concentration of ${\mathrm{S}}^{2-}$ ions in an aqueous solution is :

1. $3\times {10}^{-20}$

2. $6\times {10}^{-21}$

3. $5\times {10}^{-19}$

4. $5\times {10}^{-8}$

Q. For the following reactions, equilibrium constants are given:

$S\left(s\right)+O_2\left(g\right)\rightleftharpoons S{O}_2\left(g\right);K_1={10}^{52}$

$2S\left(s\right)+3O_2\left(g\right)\rightleftharpoons 2S{O}_3\left(g\right);K_2={10}^{129}$
Find the equilibrium constant for
$2S{O}_2+O_2\left(g\right)\rightleftharpoons 2S{O}_3\left(g\right);K_3$

<!--td {border: 1px solid #cccccc;}br {mso-data-placement:same-cell;}--> JEE MAIN 2019

1. ${10}^{154}$
2. ${10}^{181}$
3. ${10}^{25}$
4. ${10}^{77}$

Q. In which one of the following reactants, $K_p$ is less than $K_c$?

1. $2S{O}_3\left(g\right)\rightleftharpoons 2S{O}_2\left(g\right)+O_2\left(g\right)$
2. $N_2\left(g\right)+3H_2\left(g\right)\rightleftharpoons 2N{H}_3\left(g\right)$
3. $PC{l}_5\left(g\right)\rightleftharpoons PC{l}_3\left(g\right)+C{l}_2\left(g\right)$
4. $H_2\left(g\right)+I_2\left(g\right)\rightleftharpoons 2HI\left(g\right)$

Q. If a mixture 0.4 mole $H_2$ and 0.2 mole $B{r}_2$ is heated at $700\text{K}$ at equilibrium, the value of equilibrium constant is $0.25\times {10}^{10}$ then find out the ratio of concentrations of $\left(B{r}_2\right)$ and $\left(HBr\right)$ (Report your answer as $\frac{B{r}_2}{HBr}\times {10}^{11}$)

1. 70
2. 80
3. 90
4. 100

Q. For the reaction $A\left(g\right)+3B\left(g\right)\rightleftharpoons 2C\left(g\right)$ at ${27}^{o}C,$ 2 moles of A, 4 moles of B and 6 moles of C are present in 2 litre vessel. If $K_c$ for the reaction is 1.2, the reaction will proceed in:

1. Forward direction
2. Backward direction
3. The reaction will always be in equilibrium
4. none of these

Q. The equilibrium mixture for $2S{O}_2\left(g\right)+O_2\left(g\right)\rightleftharpoons 2S{O}_3\left(g\right)$ present in 1L vessel at ${600}^{o}C$ contains 0.50, 0.12, and 5.0 mole of $S{O}_2,O_2\text{and}S{O}_3$ respectively.
Calculate $K_C$ for the given change at ${600}^{o}C.$

1. $675.23mo{l}^{-1}L$
2. $765.32mo{l}^{-1}L$
3. $833.33mo{l}^{-1}L$
4. $801.23mo{l}^{-1}L$

Q. If a mixture 0.4 mole $H_2$ and 0.2 mole $B{r}_2$ is heated at $700\text{K}$ at equilibrium, the value of equilibrium constant is $0.25\times {10}^{10}$ then find out the ratio of concentrations of $\left(B{r}_2\right)$ and $\left(HBr\right)$ (Report your answer as $\frac{B{r}_2}{HBr}\times {10}^{11}$)

1. 70
2. 80
3. 90
4. 100

Q. At a certain temperature the equilibrium constant $K_c$ is 0.25 for the reaction $A_2\left(g\right)+B_2\left(g\right)\rightleftharpoons C_2\left(g\right)+D_2\left(g\right)$
If we take 1 mole of each of the four gases in a 10 litre container, what would be equilibrium concentration of $A_2\left(g\right).$

1. \N
2. 0.13
3. 0.25
4. 1

Q. For the reaction, $N_2\left(g\right)+O_2\left(g\right)\rightleftharpoons 2NO\left(g\right)$, the equilibrium constant is $K_1$. The equilibrium constant is $K_2$ for $2NO\left(g\right)+O_2\left(g\right)\rightleftharpoons 2N{O}_2\left(g\right)$. What is K for the reaction $N{O}_2\left(g\right)\rightleftharpoons \frac{1}{2}{N}_2\left(g\right)+O_2\left(g\right)$?

1. $\frac{1}{\left(K_1{K}_2\right)}$
2. $\frac{1}{\left(2K_1{K}_2\right)}$
3. $\frac{1}{\left(4K_1{K}_2\right)}$
4. ${\left(\frac{1}{K_1{K}_2}\right)}^{1/2}$

Q. The equilibrium constant for,
$2H_{2}S\left(g\right)\rightleftharpoons 2H_2\left(g\right)+S_2\left(g\right)$
is 0.0118 at 1300 K while the heat of dissociation is 597.4 kJ. The standard equilibrium constant of the reaction at 1200 K is:

1. ${10}^{-4}$
2. ${10}^{-6}$
3. ${10}^{-8}$
4. ${10}^{-10}$

Q.

If the equilibrium constant of the reaction $2HI\rightleftharpoons H_2+I_2$ is $0.25$, then the

equilibrium constant of the reaction $H_2+I_2\rightleftharpoons 2HI$ would be

1. 1.0

2. 2.0

3. 3.0

4. 4.0

Q.

At certain temperature, a compound $A{B}_2$ dissociates as: $2A{B}_{2\left(g\right)}\to 2A{B}_{\left(g\right)}+B_{2\left(g\right)}$ with a degree of dissociation $\alpha$, which is very small compared to unity. The expression of $K_p$ in terms of $\alpha$ and total pressure P is ?

1. $\frac{{\alpha }^{2}P}{2}$

2. $\frac{{\alpha }^{2}P}{3}$

3. $\frac{{\alpha }^{3}P}{3}$

4. $\frac{{\alpha }^{3}P}{2}$

Q. A container containing ammonia is allowed to decompose and the following equilibrium is established.
$2N{H}_3\left(g\right)\rightleftharpoons N_2\left(g\right)+3H_2\left(g\right)$.
Then, the equilibrium constant, $K_p$ is expressed as:
(Where $p_{N_2}$ = partial pressure of $N_2$ and $p_{N{H}_3}$ is the partial pressure of $N{H}_3$ )

1. $K_p=\frac{3^3\times p_{N_2}^2}{p_{N{H}_3}}$
2. $K_p=\frac{3^3\times p_{N_2}{p}_{H_2}^3}{p_{N{H}_3}^2}$
3. $K_p=\frac{3^3\times p_{N_2}^4}{p_{N{H}_3}^2}$
4. $K_p=\frac{3^{\left(3/2\right)}\times p_{N_2}^4}{p_{N{H}_3}^2}$

Q. For the reaction $A\left(g\right)+3B\left(g\right)\rightleftharpoons 2C\left(g\right)$ at ${27}^{o}C,$ 2 moles of A, 4 moles of B and 6 moles of C are present in 2 litre vessel. If $K_c$ for the reaction is 1.2, the reaction will proceed in:

1. Forward direction
2. Backward direction
3. The reaction will always be in equilibrium
4. none of these

Q. An aqueous solution contains 0.10 M $H_{2}S$ and 0.20 M $HCl$. If the equilibrium constants for the formation of $H{S}^{-}$from $H_{2}S$ is $1.0\times {10}^{-7}$ and that of $S^{2-}$ from $H{S}^{-}$ ions is $1.2\times {10}^{-13}$, then the concentration of $S^{2-}$ ions in aqueous solution is:

1. $5\times {10}^{-19}$
2. $5\times {10}^{-8}$
3. $3\times {10}^{-20}$
4. $6\times {10}^{-21}$

Q. Vant' Hoff equation shows the effect of temperature on equilibrium constants $K_c$ and $K_p.$ The $K_p$ varies with temperature according to the relation:

1. $log\frac{K_{p_2}}{K_{p_1}}=\frac{△H}{2.303R}\left[\frac{T_1-T_2}{T_1{T}_2}\right]$
2. $log\frac{K_{p_2}}{K_{p_1}}=\frac{△H}{2.303R}\left[\frac{T_2-T_1}{T_1{T}_2}\right]$
3. $log\frac{K_{p_2}}{K_{p_1}}=\frac{△H}{2.303R}\left[\frac{T_1{T}_2}{T_1-T_2}\right]$
4. $log\frac{K_{p_2}}{K_{p_1}}=\frac{△H}{2.303R}\left[\frac{T_1{T}_2}{T_2-T_1}\right]$

Q. The equilibrium constant $K_c$ for the reaction $P_4\left(g\right)\rightleftharpoons 2P_2\left(g\right)$ is 1.4 at ${400}^{o}C.$ Suppose that 3 mol of $P_4$ (g) and 2 mol of $P_2\left(g\right)$ are mixed in 2 L container at ${400}^{o}C.$ What is the value of reaction quotient (Q)?

1. $\frac{3}{2}$
2. $\frac{2}{3}$
3. 1
4. None of these

Q. Consider the following equilibrium in a closed container $N_2{O}_4\left(g\right)\rightleftharpoons 2N{O}_2\left(g\right)$. At a fixed temperature, the volume of the reaction container is halved. For this change, which of the following statements held true regarding the equilibrium constant $\left(K_P\right)$ and degree of dissociation $\left(\alpha \right)$:-

1. Neither $K_P$ nor $\alpha$ changes
2. Both $K_P$ and $\alpha$ changes
3. $K_P$ changes, but $\alpha$ does not change
4. $K_P$ does not change, but $\alpha$ changes

Q.

A plot of In K against $\frac{1}{T}$ (abscissa) is expected to be a straight line with intercept on ordinate axis equal to?

1. $\frac{\Delta S^{\circ }}{2.303R}$

2. $\frac{\Delta S^{\circ }}{R}$

3. $-\frac{\Delta S^{\circ }}{R}$

4. $R\times \Delta S^{\circ }$

Q. The equilibrium constants of the following are
$N_2+3H_2\rightleftharpoons 2N{H}_3;K_1$
$N_2+O_2\rightleftharpoons 2NO;K_2$

$H_2+\frac{1}{2}{O}_2\rightleftharpoons H_{2}O;K_3$
The equilibrium constant (K) of the reaction:
$2N{H}_3+\frac{5}{2}{O}_2\stackrel{K}{\rightleftharpoons }2NO+3H_{2}O$ will be

1. $K_2{K}_3^3/K_1$
2. $K_2{K}_3/K_1$
3. $K_2^3{K}_3/K_1$
4. $K_1{K}_3^3/K_2$

Q. For the zero order reaction $A\to B+C$, initial concentration of ${}^{\prime }{A}^{\prime }$ is $0.1\text{M}$. If ${}^{\prime }{A}^{\prime }$ is $0.08\text{M}$ after $10\text{minutes}$, then the half-life and completion time for the reaction, are respectively:

1. $25\text{and}50\text{min}$
2. $50\text{and}100\text{min}$
3. $70\text{and}35\text{min}$
4. $150\text{and}300\text{min}$

Q.

Equilibrium constants $K_1$ and $K_2$ for the following equilibria are

$NO\left(g\right)+0.5O_2\left(g\right)\underrightarrow{}{K}_{1}N{O}_2\left(g\right)$ and
$2N{O}_2\left(g\right)\underrightarrow{}{K}_{2}2NO\left(g\right)+O_2\left(g\right)$

1. $K_2=\frac{1}{K_1}$

2. $K_2=K_1^2$

3. $K_2=\frac{K_1}{2}$

4. $K_2=\frac{1}{K_1^2}$

Q.

Consider the following equilibria at ${25}^{\circ }C,2N{O}_{\left(g\right)}\rightleftharpoons N_{2\left(g\right)}+O_{2\left(g\right)};K_1=4\times {10}^{30}andN{O}_{\left(g\right)}+\frac{1}{2}B{r}_{2\left(g\right)}\rightleftharpoons NOB{r}_{\left(g\right)};K_2=1.4mo{l}^{-\frac{1}{2}}{L}^{\frac{1}{2}}.$ The value of K_C for the reaction (at same temperature) $\frac{1}{2}{N}_{2\left(g\right)}+\frac{1}{2}{O}_{2\left(g\right)}+\frac{1}{2}B{r}_{2\left(g\right)}\rightleftharpoons NOB{r}_{\left(g\right)}$ is :

1. $3.5\times {10}^{-31}$

2. $2.8\times {10}^{15}$

3. $7.0\times {10}^{-16}$

4. $5.6\times {10}^{30}$

Q. For the reaction, $CO\left(g\right)+C{l}_2\left(g\right)\rightleftharpoons COC{l}_2\left(g\right)$ the $\frac{K_p}{K_c}$ is equal to

1. $\sqrt{RT}$
2. $RT$
3. $\frac{1}{RT}$
4. $1.0$

Q. The approach of the following equilibrium was observed kinetically from both directions
$PtC{l}_4^{2-}+H_{2}O\rightleftharpoons Pt\left(H_{2}O\right)C{l}_3^{-}+C{l}^{-}$
At 25°C, it is found $\frac{–d\left[PtC{l}_4^{2-}\right]}{dt}=(3.9\times {10}^{-5}{s}^{-1)})\left[PtC{l}_4^{2-}\right]-(2.1\times {10}^{-3}Lmo{l}^{-1}{s}^{-1})\left[Pt\right(H_{2}O\left)C{l}_3^{-}\right]\left[C{l}^{-}\right]$
Value of $K_C$ when fourth $C{l}^{-}$ is complexed in the reaction is:

1. $1.85\times {10}^{-2}$
2. $1.86\times 2$
3. $53.85$
4. $8.19\times {10}^{-8}$