Relation between Kp and Kc

Q. For a given exothermic reaction, $K_p$ and $K_p^{\prime }$ are the equilibrium constants at temperatures $T_1$ and $T_2$ respectively. Assuming that heat of reaction is constant in temperatures range between $T_1$ and $T_2$. It is readily observation that :
(Given, $T_2>T_1$)

1. $K_P>K_P^{\prime }$
2. $K_P=K_P^{\prime }$
3. $K_{=}\frac{1}{K_P^{\prime }}$
4. $K_P<K_P^{\prime }$

Q. A solution has a $1:4$ mole ratio of pentane to hexane. The vapour pressures of the pure hydrocarbons at ${20}^0\text{C}$ are $440\text{mm Hg}$ for pentane and $120\text{mm Hg}$ for hexane. The mole fraction of pentane in the vapour phase would be:

1. $0.200$
2. $0.549$
3. $0.786$
4. $0.478$

Q. The pressure necessary to obtain $50\%$ dissociation of $PC{l}_5$ at $400K$ is numerically equal to how many times the value of the equilibrium constant $K_p$

Q.

At 450 K, $K_p=2.0\times {10}^{10}/bar$ for the given reaction at equilibrium.
$2S{O}_{2\left(g\right)}+O_{2\left(g\right)}\leftrightarrow 2S{O}_{3\left(g\right)}$
What is $K_c$ at this temperature?

Q.

For which of the following KP is less than Kc?

1. N2O4 2NO2

2. N2 + 3H2 2NH3

3. H2 + I2 2HI

4. CO + H2O CO2 + H2

Q.

Find out the value of K_c for each of the following equilibria from the value of $K_p$:
(i) $2NOCl\left(g\right)\leftrightarrow 2NO\left(g\right)+C{l}_2\left(g\right):K_p=1.8\times {10}^{-2}at500K$

Q. For which reactions at 298 K, the value of $\frac{K_p}{K_c}$ is maximum and minimum respectively.
(a) $N_2{O}_4\left(g\right)\rightleftharpoons 2N{O}_2\left(g\right)$
(b) $2S{O}_2\left(g\right)+O_2\left(g\right)\rightleftharpoons 2S{O}_3\left(g\right)$
(c) $X\left(g\right)+Y\left(g\right)\rightleftharpoons 4Z\left(g\right)$
(d) $A\left(g\right)+3B\left(g\right)\rightleftharpoons 7C\left(g\right)$

1. d, c
2. d, b
3. c, b
4. d, a

Q. The following reaction occurs in the Blast Furnace where iron ore is reduced to iron metal:

$F{e}_2{O}_3\left(s\right)+3CO\left(g\right)\rightleftharpoons 2Fe\left(s\right)+3C{O}_2\left(g\right)$

Using Le Chatelier's principle, predict which one of the following will not disturb the equilibrium?

1. Removal of $C{O}_2$
2. Removal of CO
3. Addition of $C{O}_2$
4. Addition of $F{e}_2{O}_3$

Q. Two solid compounds ${}^{\prime }{X}^{\prime }$ and ${}^{\prime }{Y}^{\prime }$ dissociates at certain temperature as follows:
$X\left(s\right)\rightleftharpoons A\left(g\right)+2b\left(g\right)K{p}_1=9\times {10}^{-3}{\text{atm}}^3$
$Y\left(s\right)\rightleftharpoons 2B\left(g\right)+C\left(g\right)K{p}_2=4.5\times {10}^{-3}{\text{atm}}^3$.
The total pressure (in atm) of gases over a mixture of ${}^{\prime }{X}^{\prime }$ and ${}^{\prime }{Y}^{\prime }$ is

1. 1.5
2. 0.45
3. 0.6
4. 0.9

Q. $N_2\left(g\right)+3H_2\left(g\right)\rightleftharpoons 2N{H}_3\left(g\right)$ is a gaseous phase equilibrium reaction taking place in a $5$ litre flask at $1atm$. For this :

1. $K_C=K_p$
2. $K_C=25K_p$
3. $K_p=25K_c$
4. $K_C=5K_p$

Q.

The $\frac{K_P}{K_C}$ ratio will be highest in case of

1. $PC{l}_5\left(g\right)\rightleftharpoons PC{l}_3\left(g\right)+C{l}_2\left(g\right)$

2. $CO\left(g\right)+\frac{1}{2}{O}_2\left(g\right)\rightleftharpoons C{O}_2\left(g\right)$

3. $H_2\left(g\right)+I_2\left(g\right)\rightleftharpoons 2Hl\left(g\right)$

4. $7H_2\left(g\right)+2N{O}_2\left(g\right)\rightleftharpoons 2N{H}_3\left(g\right)+4H_{2}O\left(g\right)$

Q. Thermal decomposition of gaseous $X_2$ to gaseous X at 298 K takes place according to the following equation:
$X_2\left(g\right)\rightleftharpoons 2X\left(g\right)$
The standard reaction Gibbs energy, ${\Delta }_r{G}^0,$ of this reaction is positive. At the start of the reaction, there is one mole of $X_2$ and no X. As the reaction proceeds, the number of moles of X formed is given by $\beta$. Thus, ${\beta }_{equilibrium}$ is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given: R = 0.083 L bar $K^{-1}mo{l}^{-1}$).

The INCORRECT statement among the following, for this reaction is:

1. Decrease in the total pressure will result in formation of more moles of gaseous X
2. At the start of the reaction, dissociation of gaseous $X_2$ takes place spontaneously
3. ${\beta }_{equilibrium}=0.7$
4. $K_c<1$

Q. Consider the following reaction system which is taking place in a closed vessel at constant temperature.
$A\left(g\right)+B\left(g\right)\rightleftharpoons AB\left(g\right)$
Which of the following is NOT true about this system at equilibrium?

1. Increasing the volume will produce more $AB$
2. Increasing the volume will produce less $AB$
3. Increasing the pressure will produce more $AB$
4. There is no effect of increasing pressure or volume.

Q. $K_p$ for a reaction at ${25}^{o}C$ in 10 atm is 8.568. Then $K_c$ for the reaction at ${25}^{o}C$ will be:
$N_2\left(g\right)+3H_2\left(g\right)\to 2N{H}_3\left(g\right)$

1. $4.33\times {10}^{-1}M$
2. $3.33\times {10}^{-2}M$
3. $3.89\times {10}^{-1}M$
4. none of these

Q. Solid ammonium carbamate, $N{H}_{4}C{O}_{2}N{H}_2\left(s\right)$, dissociates into ammonia and carbon dioxide when it evaporates as shown by
$N{H}_{4}C{O}_{2}N{H}_2\left(s\right)\rightleftharpoons 2N{H}_3\left(g\right)+C{O}_2\left(g\right)$
At ${25}^{\circ }C$, the total pressure of the gases in equilibrium with the solid is $0.116\text{atm}$, if $0.1\text{atm}$ of $C{O}_2$ is introduced after equilibrium is reached then:

1. The final pressure of $C{O}_2$ will be less than $0.1\text{atm}$
2. The final pressure of $C{O}_2$ will be more than $0.1\text{atm}$
3. The pressure of $N{H}_3$ will decrease due to addition of $C{O}_2$
4. The pressure of $N{H}_3$ will increase due to addition of $C{O}_2$

Q. In the given reaction sequence


Number of moles (n) of phenyl hydrazine consumed is

Q.

Cassiterite when reduced with coke Tin is obtained. What is the minimum temperature needed for the reduction of cassiterite would take place?

At 298 K ${∆}_{\mathrm{f}}\mathrm{H}°=\left({\mathrm{SnO}}_2\left(\mathrm{S}\right)\right)=-580.0{\mathrm{kJmol}}^{-1},{∆}_{\mathrm{f}}\mathrm{H}°\left({\mathrm{CO}}_2\left(\mathrm{g}\right)\right)=-394.0{\mathrm{kJmol}}^{-1}$

$\mathrm{S}°\left({\mathrm{SnO}}_2\left(\mathrm{s}\right)\right)=56.0{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1},\mathrm{S}°\left(\mathrm{Sn}\left(\mathrm{s}\right)\right)=52.0{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$

$\mathrm{S}°\left(\mathrm{C}\left(\mathrm{s}\right)\right)=6.0{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1},°\left({\mathrm{CO}}_2\left(\mathrm{g}\right)\right)=210.0{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$

Assume that enthalpies and entropies are temperature independent.

Q. How many moles of nitric acid are required to convert $1mol$ of sulfur to sulfuric acid?

1. $10$
2. $4$
3. $48$
4. $20$

Q. $I_2$ gets $5\%$ dissociated into atoms when1.0 mole of $I_2\left(g\right)$

is introduced into an evacuated flask of 1 L capacity at 150K.The $K_p$for the reaction $I_2\left(g\right)\rightleftharpoons 2I\left(g\right)$ at 150K is:

1. 
2. 
3. 
4. 

Q.

Which of the following is correct for given curve?

1. $\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$m$}\right.\right)\alpha \left(P\right)\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

2. $\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$m$}\right.\right)\alpha \left(P\right)$

3. $\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$m$}\right.\right)\alpha {\left(P\right)}^2$

4. $\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$m$}\right.\right)\alpha {\left(P\right)}^0$

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 holds true regarding the equilibrium constant $K_p$ and degree of dissociation $\left(\alpha \right)$?

1. neither $K_p$ nor $\alpha$ changes
2. both $K_p$ and $\alpha$ change
3. $K_p$ changes, but $\alpha$ does not changes
4. $K_p$ does not change, but $\alpha$ changes

Q. Find out the value of $K_c$ for the given equilibria (i) and (ii) respectively:
$\left(i\right)2NOCl\left(g\right)\rightleftharpoons 2NO\left(g\right)+C{l}_2\left(g\right);K_P=1.8\times {10}^{-2}at500K$
$\left(ii\right)CaC{O}_3\left(s\right)\rightleftharpoons CaO\left(s\right)+C{O}_2\left(g\right);K_p=167at1073K$

($R=0.0831barLmo{l}^{-1}{K}^{-1}$)

1. $4.38\times {10}^{-4}and1.87$
2. $8.8\times {10}^{-4}and3.8$
3. $4.38\times {10}^{4}and1.87$
4. $8.8\times {10}^{4}and3.8$

Q.

Suppose $\text{det}\left[\begin{array}{cc}\underset{k=0}{\overset{n}{\sum k}}& \sum _{k=0}^n{}^n{C}_k{k}^2\\ \sum _{k=0}^n{}^n{C}_{k}k& \sum _{k=0}^n{}^n{C}_k{3}^k\end{array}\right]=0$ holds for some positive integer $n$. Then $\sum _{k=0}^n\frac{{}^n{C}_k}{k+1}$ equals.

Q. Identify the correct statement(s)

1. Low pressure is favourable for evaporation of $H_{2}O\left(l\right).$
2. On adding graphite to an equilibria involving $C\left(s\right),O2\left(g\right)$ and $C{O}_2\left(g\right)$ more $C{O}_2\left(g\right)$ will be formed.
3. For the reaction: $3Fe\left(s\right)+4H_{2}O\left(g\right)\rightleftharpoons F{e}_3{O}_4\left(s\right)+4H_2\left(g\right)$ $K_P$ and $K_C$ will be same.
4. Normal boiling point of water will be more than standard boiling point of water.

Q. What is the difference between $\Delta$H and $\Delta$U? What is the sign of $\Delta$H for exothermic and endothermic reactions? Under what circumstances $\Delta$H = $\Delta$U?

Q. $K_p$ for a reaction at ${25}^{o}C$ in 10 atm is 8.568. Then $K_c$ for the reaction at ${25}^{o}C$ will be:
$N_2\left(g\right)+3H_2\left(g\right)\to 2N{H}_3\left(g\right)$

1. $4.33\times {10}^{-1}M$
2. $3.33\times {10}^{-2}M$
3. $3.89\times {10}^{-1}M$
4. none of these

Q. The relation between $K_p$ and $K_c$ for the following reactions.
$\left(i\right)N_2\left(g\right)+3H_2\left(g\right)\rightleftharpoons 2N{H}_3\left(g\right)$
$\left(ii\right)2H_{2}O\left(g\right)\rightleftharpoons 2H_2\left(g\right)+O_2\left(g\right)$
For these two reactions;
(i) $K_{p_1}=K_c(RT{)}^x$
(ii) $K_{p_2}=K_c(RT{)}^y$

Find the sum (x+y).

1. $-1$
2. $1$
3. $2$
4. $-1.5$

Q.

In which of the following reaction, the value of $K_p$ will be equal to $K_c$

1. H₂ + I₂ 2HI

2. PCl₅ PCl₃ + Cl₂

3. 2SO₂ + O₂ 2SO₃

4. 2NH₃ N₂ + 3H₂

Q. Find out the value of $K_c$ for the given equilibria (i) and (ii) respectively:
$\left(i\right)2NOCl\left(g\right)\rightleftharpoons 2NO\left(g\right)+C{l}_2\left(g\right);K_P=1.8\times {10}^{-2}at500K$
$\left(ii\right)CaC{O}_3\left(s\right)\rightleftharpoons CaO\left(s\right)+C{O}_2\left(g\right);K_p=167at1073K$

($R=0.0831barLmo{l}^{-1}{K}^{-1}$)

1. $8.8\times {10}^{-4}and3.8$
2. $8.8\times {10}^{4}and3.8$
3. $4.38\times {10}^{-4}and1.87$
4. $4.38\times {10}^{4}and1.87$

Q. For the reaction
$N_2\left(g\right)+3H_2\left(g\right)\rightleftharpoons 2N{H}_3\left(g\right);△H=-46kJmo{l}^{-1}$
Calculate the value of $K_p.$

Given $K_C=0.5li{t}^{2}mo{l}^{-2}$ and $R=0.082Latmmo{l}^{-1}{K}^{-1}$ at ${400}^{o}C$

1. $1.64\times {10}^{-4}$
2. $2.64\times {10}^{-4}$
3. $0.64\times {10}^{-4}$
4. $1.34\times {10}^{-4}$