Derivation of Kp and Kc

Q. Consider the reaction
$N_2\left(g\right)+3H_2\left(g\right)\rightleftharpoons 2N{H}_3\left(g\right)$
The equilibrium constant of the above reaction is $K_p.$ If pure ammonia is left to dissociate, the partial pressure of ammonia at equilibrium is given by: (Assume that ) $P_{N{H}_3}<<P_{total}$ at equilibrium)

1. $\frac{3^{3/2}{K}_p^{1/2}{P}^2}{2^4}$
2. $\frac{3^{3/2}{K}_p^{1/2}{P}^2}{2^2}$
3. $\frac{K_p^{1/2}{P}^2}{2^2}$
4. $\frac{K_p^{1/2}{P}^2}{2^4}$

Q.

The dissociation equilibrium of a gas ${\mathrm{AB}}_2$ can be represented as:

$2{\mathrm{AB}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{AB}\left(\mathrm{g}\right)+{\mathrm{B}}_2\left(\mathrm{g}\right)$
The degree of dissociation is $\mathrm{x}$ and is small compared to $1$. The expression relating the degree of dissociation $\mathrm{x}$ with equilibrium constant ${\mathrm{K}}_{\mathrm{p}}$ and total pressure $\mathrm{p}$ is?

Q. 24 The rate constant k1 and k2 for two different reactions are 10*16 e*-2000/T and 10*15 e *-1000/T respectively . the temperature at which k1 =k2

Q. Balance the following equation by ion electron method--
KMnO₄ + FeSO₄ + H₂SO₄ -----> Fe₂(SO₄)₃ + K₂SO₄ + H₂O​​

Q. $4.0$ moles of argon and $5.0$ moles of $PC{l}_5$ are introduced into an evacuated flask of $100$ litre capacity at $610\text{K}$. The system is allowed to equilibrate. At equilibrium, the total pressure of mixture was found to be $6.0\text{atm}$. The $K_p$ for the reaction is
[Given : $R=0.082Latm{K}^{–1}mo{l}^{–1}$]

1. $6.24$
2. $12.13$
3. $15.24$
4. $2.25$

Q. For the dissociation reaction, $N_2{O}_4\rightleftharpoons 2N{O}_2\left(g\right)$, the equilibrium constant $K_p$ is 0.120 atm at 298 K and total pressure of system is 2 atm. Calculate the degree of dissociation of $N_2{O}_4$.

1. $0.586$
2. $0.121$
3. $0.150$
4. $0.254$

Q. When limestone is heated, quicklime is formed according to the equation.
$CaC{O}_3\left(s\right)\rightleftharpoons CaO\left(s\right)+C{O}_2\left(g\right)$
The experiment was carried out in the temperature range $800-{900}^{o}C,$ Equilibrium constant $K_p$ follows the relation. $log{K}_p=7.282-\frac{8500}{T}$
where, T is temperature in Kelvin. At what temperature the decomposition will give $C{O}_2\left(g\right)$ at 1 atm?

1. ${894.11}^{o}C$
2. ${794.66}^{o}C$
3. ${987.18}^{o}C$
4. ${635.45}^{o}C$

Q.

Write the expression for the equilibrium constant, $K_C$ for each of the following reactions:

(i) $2NOCl\left(g\right)\leftrightarrow 2NO\left(g\right)+C{l}_2\left(g\right)$

(ii) $2Cu\left(N{O}_3{)}_2\right(aq)\leftrightarrow 2CuO(S)+4N{O}_2(g)+O_2(g)$

(iii) $C{H}_{3}COO{C}_2{H}_5\left(aq\right)+H_{2}O\left(l\right)\leftrightarrow C{H}_{3}COOH\left(aq\right)+C_2{H}_{5}OH\left(aq\right)$

(iv) $F{e}^{3+}\left(aq\right)+3O{H}^{-}\left(aq\right)\leftrightarrow Fe\left(OH{)}_3\right(s)$

(v) $I_2\left(s\right)+5F_2\leftrightarrow 2I{F}_5$

Q. $\log \frac{K_P}{K_C}+\log RT=0$ is a relationship for the reaction:

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

Q. The rate law for reaction between the substances A and B is given by Rate = $K\left[A{]}^n\right[B{]}^m$. On doubling the concentration of A and halving the concentration of B, the ratio of the new rate to the earlier rate of reaction will be

1. $n-m$
2. $m+n$
3. $2^{n-m}$
4. $\frac{1}{2^{m+n}}$

Q. The value of $K_p$ for the reaction
$2H_{2}O\left(g\right)+2C{l}_2\left(g\right)\rightleftharpoons 4HCl\left(g\right)+O_2\left(g\right)$ is 0.03 atm at ${427}^{\circ }C$, when the partial pressure are expressed in atmosphere, then the value of $K_c$ for the same reaction is

1. $5.23\times {10}^{-4}$
2. $7.34\times {10}^{-4}$
3. $3.2\times {10}^{-3}$
4. $5.43\times {10}^{-5}$

Q. Choose the correct option:
Here,
$t_{1/2}$ is the half life period of the reaction

1. For a first order reaction, $t_{1/2}$ is directly proportional to initial concentration
2. For a zero order reaction , $t_{1/2}$ is inversely proportional to initial concentration
3. For a second order reaction, $t_{1/2}$ is inversely proportional to initial concentration
4. All of the above

Q.

Why do solids not affect equilibrium?

Q. One mole of $H_{2}O$ and one mole of CO are taken in 10 L vessel and heated to 725 K. At equilibrium 40% of water reacts with CO according to the equation,
$H_{2}O\left(g\right)+CO\left(g\right)\rightleftharpoons H_2\left(g\right)+C{O}_2\left(g\right)$. What is the value of equilibrium constant $\left(K_c\right)$ for the reaction?

1. 44
2. 2.22
3. 4.4
4. 0.44

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.

At 473 K, equilibrium constant Kc for decomposition of phosphorus pentachloride, $PC{l}_{5}is8.3\times {10}^{-3}$. If decomposition is depicted as,
$PC{l}_5\left(g\right)\leftrightarrow PC{l}_3\left(g\right)+C{l}_2\left(g\right){\Delta }_r{H}^{\circ }=124.0kJmo{l}^{-1}$

Write an expression for $K_c$ for the reaction.

What is the value of $K_c$ for the reverse reaction at the same termperature?

What would be the effect on $K_c$ if
(i) more $PC{l}_5$ is added
(ii) pressure is increased?
(iii) The temperature is increased?

Q. HI was heated in a sealed tube at ${440}^{o}C$ till the equilibrium was established. The dissociation of HI was found to be 22%. According to following reaction,
$2HI\rightleftharpoons H_2+I_2$. The equilibrium constant for dissociation is -

1. 0.282
2. 0.0786
3. 0.0199
4. 1.99

Q.

Ammonium carbonate decomposes as
$N{H}_{2}COON{H}_4\left(s\right)\leftrightharpoons 2N{H}_3\left(g\right)+C{O}_2\left(g\right)$ For the reaction, $K_P=2.9\times {10}^{-5}at{m}^3$. Calculate the total pressure at equilibrium if $1moleofN{H}_{2}COON{H}_4$is taken.

1. 0.0766 atm
2. 0.0582 atm
3. 0.0388 atm
4. 0.0194 atm

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.

A sample of HI_{(g)} is placed in flask at a pressure of 0.2 atm. At equilibrium the partial pressure of HI_{(g)} is 0.04 atm. What is K_p for the given equilibrium?
$2HI\left(g\right)\leftrightarrow H_2\left(g\right)+I_2\left(g\right)$

Q.

Bromine monochloride, BrCl decomposes into bromine and chlorine and reaches the equilibrium:
$2BrCl\leftrightarrow B{r}_2\left(g\right)+C{l}_2\left(g\right)$
Fro which $K_c=32$ at 500 K.
If initially pur BrCl is present at a concentration of $3.3\times {10}^{-3}mo{l}^{-1}$, what is its molar concentration in the mixture at equilibrium?

Q. At 700 K, the equilibrium constant $K_p,$ for the reaction
$2S{O}_3\left(g\right)\rightleftharpoons 2S{O}_2\left(g\right)+O_2\left(g\right)$
is $1.8\times {10}^{-3}kPa.$ What is the numerical value of $K_C$ for this reaction at the same temperature?
$R=0.0821Latmmo{l}^{-1}{K}^{-1}$

1. $3.09\times {10}^{-7}molelitr{e}^{-1}$
2. $9.03\times {10}^{-7}molelitr{e}^{-1}$
3. $5.05\times {10}^{-9}molelitr{e}^{-1}$
4. $5.05\times {10}^{-5}molelitr{e}^{-1}$

Q. Derivation of rate cons†an t for nth order of reactio

Q. In the reaction, $C\left(s\right)+C{O}_2\left(g\right)\rightleftharpoons 2CO\left(g\right),$ the equilibrium pressure is 12 atm. If 50% of $C{O}_2$ reacts then $K_p$ will be:

1. 20 atm
2. 24 atm
3. 12 atm
4. 16 atm

Q. If concentration of $O{H}^{-}$ions in the reaction $Fe\left(OH{)}_3\right(s)\leftrightharpoons F{e}^{3+}+(aq)+3O{H}^{-}(aq)$ is decreased by $1/4$ times, then equilibrium concentration of $F{e}^{3+}$will increase by

1. 8 times
2. 16 times
3. 64 times
4. 4 times.

Q. 26.The molecular mass of O2 and SO2 are 32 and 64 respectively.If one litre of O2 at at 15 degree ceisius and 750mm pressure contains N molecules, the number of molecules in two litres of S02 under the same conditions of temperature and pressure will be A N/2 B 4N C N D 2N

Q. A vessel at 1000 K contains carbon dioxide with a pressure of 0.5 atm. Some of the carbon dioxide is converted to carbon monoxide on addition of graphite.
$C{O}_2+C\rightleftharpoons 2CO$
Calculate the value of $K_p$ if total pressure at equilibrium is 0.8 atm.

1. 2.5 atm
2. 1.1 atm
3. 0.5 atm
4. 1.8 atm

Q. 39.The rate of reaction increases to 2.3 times when the temperature is raised from 300k to 310k. If K is the rate constant at 300k then the rate constant at 310k will be equal to-

Q.

$K_p=0.04$ atm at 899 K for the equilibrium shown below. What is the equilibrium concentration of $C_2{H}_6$ when it is placed in a flask at 4.0 atm pressure and allowed to come to equilibrium?
$C_2{H}_6\left(g\right)\leftrightarrow C_2{H}_4\left(g\right)+H_2\left(g\right)$

Q. The ratio of $K_p/K_c$ for the reaction, $CO\left(g\right)+\frac{1}{2}{O}_2\left(g\right)\rightleftharpoons C{O}_2\left(g\right)$ is

1. $1$
2. $RT$
3. $(RT{)}^{1/2}$
4. $(RT{)}^{-1/2}$