Derivation of Kp and Kc

Q. Consider the reactions,
$N{O}_2\left(g\right)\rightleftharpoons \frac{1}{2}{N}_2\left(g\right)+O_2\left(g\right)\cdots K_1$
$N_2{O}_4\left(g\right)\rightleftharpoons 2N{O}_2\left(g\right)\cdots K_2$
Give the expression for equilibrium constant for the formation of $N_2{O}_4$ from $N_2$ and $O_2$:

1. $\frac{1}{2K_1}+\frac{1}{K_2}$
2. $\sqrt{\frac{1}{K_1{K}_2}}$
3. $\frac{K_2}{K_1}$
4. $\frac{1}{K_1^2}\times \frac{1}{K_2}$

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. both and changes

2. changes, but does not change

3. does not change, but changes

4. neither nor changes

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 2$N{H}_3$ (g) ⇌ $N_2$(g) + 3$H_2$(g), if the total equilibrium pressure is P and degree of dissociation is α, the equilibrium constant $K_p$ is given by

$\frac{27{\alpha }^4{p}^2}{16{(1-{\alpha }^2)}^2}$

1. True

2. False

Q. Consider the following reactions in which all the reactants and products are in gaseous state.
$2PQ\leftrightharpoons P_2+Q_2;K_1=2.5\times {10}^5$
$PQ+\frac{1}{2}{R}_2\leftrightharpoons PQR,K_2=5\times {10}^{-3}$

The value of K₃ for the equilibrium
$1/2P_2+1/2Q_2+1/2R_2\leftrightharpoons PQR$

1. 2.5 x 10^-3
2. 2.5 x 10³
3. 1.0 x 10^-5
4. 5 x 10³

Q. For a hypothetical reaction
$4A+5B\leftrightharpoons 4P+6Q,$
The equilibrium constant $K_c$ has units

1. mol L^-1
2. mol^-1L
3. unit less
   
4. (mol L^-1)^-2

Q.

At 298 K and 1 atm pressure, the partial pressures in an equilibrium mixture of $N_2{O}_4$ and $N{O}_2$ are 0.7 and 0.3 atmosphere respectively. What will be the partial pressure of $N{O}_2$ when the gases are in equilibrium at 298 K and at a total (equilibrium) pressure of 10 atmospheres?

1. 2.23 atm

2. 1.078 atm

3. 1.60 atm

4. 0.77 atm

Q. Hl was heated in a closed tube at ${440}^{\circ }c$ till equilibrium is obtained. At this temperature $22\%$ of Hl was dissociated. The equilibrium constant for this dissociation will be

1. 0.0199
2. 1.99
3. 0.282
4. 0.0796

Q. In a reaction $A+2B\leftrightharpoons 2C;2molesofA,3$ mole of $Band2moleofC$ are placed in a 2 L flask and the equilibrium concentration of $Cis0.5mole/L.$ The equilibrium constant K for the reaction is:

1. 0.147
2. 0.026
3. 0.05
4. 0.073

Q.

The equilibrium constant $k_c$ of the reaction $A_2$ (g) + $B_2$ (g) $\rightleftharpoons$ 2AB (g) is 50. If 1 mol of $A_2$ and 2 mol of $B_2$ are mixed, the amount of AB at equilibrium would be:

1. .934 mol

2. .467 mol

3. 1.4 mol

4. 1.867 mol