Derivation of Kp and Kc

Q. For the reaction $PC{l}_3\left(g\right)+C{l}_2\left(g\right)\rightleftharpoons PC{l}_5\left(g\right),$
The mole of each component $PC{l}_5,PC{l}_{3}andC{l}_2$ at equilibrium were found to be 2. If the total pressure is 3 atm. The value of $K_P$ will be-

1. 1 atm
2. 2 atm
3. 3 atm
4. 1.5 atm

Q. The expression of $K_C$ for the following reaction is :
$CaC{O}_3\left(s\right)\rightleftharpoons CaO\left(s\right)+C{O}_2\left(g\right)$

1. $K_c=\frac{\left[CaO\right]\times \left[C{O}_2\right]}{\left[CaC{O}_3\right]}$
2. $K_c=\frac{[C{O}_2{]}^2}{\left[CaC{O}_3\right]}$
3. $K_c=\left[C{O}_2\right]$
4. None of the above

Q. What is $K_c$ for the following equilibrium when the equilibrium concentration of each substance is: $\left[S{O}_2\right]=0.60M,\left[O_2\right]=0.82M$ and $\left[S{O}_3\right]=1.90M$ ?
$2S{O}_2+O_2\rightleftharpoons 2S{O}_3$

1. $12.24M^{-1}$
2. $1.23M^{-1}$
3. $22.23M^{-1}$
4. $32.23M^{-1}$

Q. Pure $PC{l}_5$ is introduced into an evacuated chamber and comes to equilibrium at ${247}^{\circ }\text{C}$ and $2.0atm$. The equilibrium gaseous mixture contains $40\%$ chlorine by volume. Calculate $K_p$ at ${247}^{\circ }\text{C}$ for the reaction
$PC{l}_5\left(g\right)\rightleftharpoons PC{l}_3\left(g\right)+C{l}_2\left(g\right)$

1. $0.625atm$
2. $4atm$
3. $1.6atm$
4. None of these

Q. $K_c$ for the reaction $N_2{O}_4\rightleftharpoons 2N{O}_2$ in chloroform at 291 K is 1.14. Calculate the $K_p$ of the reaction when the concentration of the two gases are $0.5mold{m}^{-3}$ each at the same temperature. $(R=0.082Latm{K}^{-1}mo{l}^{-1})$

1. -27.1
2. -19.6
3. 1.1
4. 27.1

Q.

The equilibrium constant in a reversible reaction at a given temperature

1. It is not characteristic of the reaction

2. Depends on the concentration of the products at equilibrium

3. Depends on the initial concentration of the reactants

4. Does not depend on the initial concentrations

Q.

For the reaction $CaC{O}_3$(s) $\leftrightharpoons$ $CaO$(s) + $C{O}_2$(g) the partial pressure of $C{O}_2$ (at equilibrium) depends on:

1. the mass of $CaO$

2. the mass of $CaC{O}_3$

3. Both a and b

4. temperature

Q. which of the following values of equilibrium constant predict almost completion of reaction 1] 10^-2 2]10^0 3]10 4]10^4

Q. 26.In a reversible reaction A(g)+B(g)--->C(g). Initially 1 mol of each reactant is taken in 2L container if at equilibrium 20% of A reacts with B. Then what will be equilibrium constant Kc for the reaction

Q. Two gases A and B having the same volume diffuse through a porous partition in 20 and 10 secondsrespectively. The molecular mass of A is 49 u.Molecular mass of B will be

Q. $2N{H}_3\left(g\right)\rightleftharpoons N_2\left(g\right)+3H_2\left(g\right)$ If 'a' moles of $N{H}_3$ are given initially. Let x moles of $N{H}_3$ are decomposed at equilbrium and $Vlitre$ be the capacity of vessel in which reaction is being studied. Find out the value of $K_c$.

1. $\frac{27x^2}{16V^2(a-x)}$
2. $\frac{27x^4}{16V^2(a-x{)}^2}$
3. $\frac{27x^4}{16V^4(a-x{)}^2}$
4. $\frac{27x^2}{16V^2(a-x{)}^2}$

Q. 2 moles of $PC{l}_5,$ were heated in a closed vessel of 2 litre capacity. At equilibrium, 40% of $PC{l}_5$ is dissociated into $PC{l}_{3}andC{l}_2.$ The value of equilibrium constant is

1. 0.266
2. 0.53
3. 2.66
4. 5.3

Q.

During the kinetic study of the reaction, $2\mathrm{A}+\mathrm{B}$ give $\mathrm{C}+\mathrm{D}$ following results were obtained.

Run	$\left[\mathrm{A}\right]$ in $\mathrm{M}$	$\left[\mathrm{B}\right]$ in $\mathrm{M}$	Initial rate of formation of $\mathrm{D}$ in ${\mathrm{Ms}}^{-1}$
1	0.1	0.1	$6.0\times {10}^{-3}$
2	0.3	0.2	$7.2\times {10}^{-2}$
3	0.3	0.4	$2.88\times {10}^{-1}$
4	0.4	0.1	$2.40\times {10}^{-2}$

On the basis of the above data which one is correct?

1. $\mathrm{r}=\mathrm{k}{\left[\mathrm{A}\right]}^2\left[\mathrm{B}\right]$

2. $\mathrm{r}=\mathrm{k}\left[\mathrm{A}\right]\left[\mathrm{B}\right]$

3. $\mathrm{r}=\mathrm{k}{\left[\mathrm{A}\right]}^2{\left[\mathrm{B}\right]}^2$

4. $\mathrm{r}=\mathrm{k}\left[\mathrm{A}\right]{\left[\mathrm{B}\right]}^2$

Q. A mixture of 0.373 atm of NO(g) and 0.31 atm of $C{l}_2\left(g\right)$ is prepared at $500K$. The reaction $2NO\left(g\right)+C{l}_2\left(g\right)\rightleftharpoons 2NOCl\left(g\right)$ takes place. The total pressure at equilibrium is 0.544 atm. Determine $K_p$ for the reaction.

1. $50.08at{m}^{-1}$
2. $10.08at{m}^{-1}$
3. $50.07at{m}^{-1}$
4. None of the above

Q.

In the reversible reaction A + B $\rightleftharpoons$​ C + D, the concentration of each C and D at

equilibrium was 0.8 mole/litre, then the equilibrium constant $K_C$ will be

1. 6.4

2. 0.64

3. 1.6

4. 16.0

Q. At a certain temperature and a total pressure of ${10}_5$ Pa, iodine vapours contain $40\%$ by volume of iodine atoms
$\left[I_2\right(g)\leftrightharpoons 2I(g\left)\right].K_p$ for the equilibrium will be

1. $0.67$
2. $1.5$
3. $2.67\times {10}^4$
4. $9.0\times {10}^4$

Q. A reaction at equilibrium involving 2 moles each of $PC{l}_5,PC{l}_3,$ and $C{l}_2$ is maintained at ${250}^{o}C$ and a total pressure of 3 atm. The value of $K_p$ is :
Given: $PC{l}_5\rightleftharpoons PC{l}_3+C{l}_2$

1. 5
2. 4
3. 8
4. 1

Q. For the hypothetical reactions, the equilibrium constant (K) values are given:
$A\rightleftharpoons B;K_1=2;B\rightleftharpoons C;K_2=4;C\rightleftharpoons D;K_3=3$
The equilibrium constant (K) for the reaction $A\rightleftharpoons D$ is:

1. 48
2. 6
3. 24
4. 12

Q. Solid ammonium carbamate dissociates into $N{H}_3$ and $C{O}_2$ as $N{H}_{2}COON{H}_4\rightleftharpoons N{H}_3\left(g\right)+C{O}_2\left(g\right).$ The total pressure at equilibrium is 5 atm. Calculate the equilibrium constnat $K_p.$

1. $37.04at{m}^2$
2. $22.52at{m}^2$
3. $18.52at{m}^2$
4. $45.04at{m}^2$

Q.

Consider the following equilibrium in a closed container:

$N_2{O}_4$ (g) $\leftrightharpoons$ $2N{O}_2$ (g)

At a fixed temperature, the volume of the reaction container is halved. For this change, which of the following statements holds true regarding the equilibrium constant $K_p$ and degree of dissociation $\alpha$?

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. The standard enthalpy and entropy changes for the reaction in equilibrium for the forward direction are given below:
$CO\left(g\right)+H_{2}O\left(g\right)\rightleftharpoons C{O}_2\left(g\right)+H_2\left(g\right)$
$△H_{300K}^o=-41.16kJmo{l}^{-1}$
$△S_{300K}^o=-4.24\times {10}^{-2}kJmo{l}^{-1}$
Calculate $K_p$ (at 300 K.)

1. $4.93\times {10}^4$
2. $8.93\times {10}^{-4}$
3. $8.93\times {10}^4$
4. None of the above

Q. Equimolar concentrations of $H_{2}and{I}_2$ are heated to equilibrium in a 2litre flask. At equilibrium, the forward and backward rate constants are found to be equal. What percentage of initial concentration of $H_2$has reacted at equilibrium?

1. $33.33\%$
2. $75\%$
3. $50\%$
4. $15\%$

Q. If a mixture of $N_2$ and $H_2$ in the ratio 1 : 3 at 50 atmosphere and ${650}^{o}C$ is allowed to react till equilibrium is reached. Ammonia present at equilibrium was at 25 atm pressure. Calculate the equilibrium constant ($K_P$) for the reaction.
$N_{2\left(g\right)}+3H_{2\left(g\right)}\rightleftharpoons 2N{H}_{3\left(g\right)}$

1. $1.677\times {10}^{-3}at{m}^{-2}$
2. $2.677\times {10}^{-3}at{m}^{-2}$
3. $0.677\times {10}^{-3}at{m}^{-2}$
4. $3.677\times {10}^{-3}at{m}^{-2}$

Q. Choose the correct expression of $K_p$ for reaction,
$4N{H}_3\left(g\right)+5O_2\left(g\right)\rightleftharpoons 4NO\left(g\right)+6H_{2}O\left(g\right)$

1. $K_p=\frac{\left[P_{NO}{]}^4\right[P_{H_{2}O}{]}^6}{\left[P_{N{H}_3}{]}^4\right[P_{O_2}{]}^5}$
2. $K_p=\frac{\left[P_{N{H}_3}{]}^4\right[P_{O_2}{]}^5}{\left[P_{NO}{]}^4\right[P_{H_{2}O}{]}^6}$
3. $K_p=\frac{\left[P_{N{H}_3}\right]\left[P_{O_2}\right]}{\left[P_{NO}\right]\left[P_{H_{2}O}\right]}$
4. $K_p=\frac{\left[P_{NO}\right]\left[P_{H_{2}O}\right]}{\left[P_{N{H}_3}\right]\left[P_{O_2}\right]}$

Q. A sample of $HI\left(g\right)$ is placed in a flask at a pressure of $0.2atm$. At equilibrium the partial pressure of $HI\left(g\right)$ is $0.04atm$. What is $K_p$ for the given equilibrium?

Q. At ${30}^{\circ }C,K_p$ for the dissociation reaction:
$S{O}_{2}C{l}_2\left(g\right)\leftrightharpoons S{O}_2\left(g\right)+C{l}_2\left(g\right)is2.9x{10}^{-2}$~atm. If the total pressure is 1 atm, the degree of dissociation of $S{O}_{2}C{l}_{2}is(assume1-{\alpha }^2=1)$

1. $85\%$
2. $12\%$
3. $17\%$
4. $35\%$

Q.

The thermal decomposition of $N_2{O}_4$g) $\leftrightharpoons$ 2$N{O}_2$ (g) is as shown below:

$\begin{array}{cc}& N_2{O}_4\left(g\right)\rightleftharpoons 2N{O}_2\left(g\right)\\ Atstart& amol0mol\\ Atequb.& (a-x)mol2xmol\end{array}$

Where x = degree of dissociation. If V and P are equilibrium volume and pressure respectively then the corresponding expressions for K_c and K_p are $\frac{4x^2}{V(a-x)}$ and $\frac{4x^2}{a^2-x^2}$ (respectively). True or False?

1. True

2. False

Q. For the reaction
$A\left(g\right)+B\left(g\right)\rightleftharpoons 2C\left(g\right)$
The equilibrium concentration of A and B each is $0.2mol{L}^{-1}$ and concentration of C is observed as $0.60mol{L}^{-1}$ Equilibrium constant $K_c$ will be :

1. 9
2. 18
3. 6
4. 24

Q.

2 moles of $PC{l}_5$ were heated in a closed vessel of 2 litre capacity. At

equilibrium, 40% of $PC{l}_5$ is dissociated into $PC{l}_3$ and $C{l}_2$. The value of

equilibrium constant is

1. 0.53

2. 2.66

3. 0.266

4. 5.3

Q. In a container equilibrium
$N_2{O}_4\left(g\right)\rightleftharpoons 2N{O}_2\left(g\right)$
is attained at ${25}^{o}C.$ The total equilibrium pressure in container is 380 torr. If equilibrium constant of above equilibrium is 0.667 atm, then degree of dissociation of $N_2{O}_4$ at this temperature will be:

1. $\frac{1}{3}$
2. $\frac{1}{2}$
3. $\frac{2}{3}$
4. $\frac{1}{4}$