Tag: relationship between equilibrium constant, reaction quotient and gibbs energy

Questions Related to relationship between equilibrium constant, reaction quotient and gibbs energy

The equilibrium constant $K p$ for the reaction $2H _2(g) + O _2(g)  \rightleftharpoons 2H _2O(g)$ at 2000 K is $1.6 \times 10^7$. The equilibrium constant of the reaction $H _2O(g)  \rightleftharpoons H _2(g) + \frac{1}{2} O _2(g)$ is _______.

chemistry chemical equilibrium relationship between equilibrium constant, reaction quotient and gibbs energy law of mass action chemical equilibrium and acids-bases

  1. $6.25 \times 10^{-8}$

  2. $2.5 \times 10^{-4}$

  3. $7.5 \times 10^{-12}$

  4. $4\times 10^{-6}$

Show answer
Correct Option: B
Explanation:

For the reaction, $2H _2(g) + O _2(g)  \rightleftharpoons 2H _2O(g)$,
$K = \dfrac{{[H _2O]}^{2} _{}} {{[H _2]}^{2} _{} [{O} _{2}]}$

$2H _2O(g)  \rightleftharpoons 2H _2(g) + O _2(g)$
$K = \dfrac{{[H _2]}^{2} _{} [{O} _{2}]}{[{H _2O}]^{2} _{}}$

$H _2O(g)  \rightleftharpoons H _2(g) + \frac{1}{2} O _2(g)$
$K _1 = \sqrt{\dfrac{{[H _2O]}^{2} _{}} {{[H _2]}^{2} _{} [{O} _{2}]}}$

Thus, $K _1 = \dfrac{1}{\sqrt{1.6107}}$$= 2.5 \times 10^{-4}$

Which of the following is true about the reaction quotient?

chemistry chemical equilibrium relationship between equilibrium constant, reaction quotient and gibbs energy law of mass action chemical equilibrium and acids-bases

  1. It relates the ratio of the concentrations of products to reactants once the reaction has reached chemical equilibrium.

  2. It is always equal to the equilibrium constant.

  3. It can never be equal to the equilibrium constant.

  4. It relates the concentrations of products to reactants at any point in time.

  5. None of these answers are correct

Show answer
Correct Option: D
Explanation:

The reaction quotient relates the concentrations of products to reactants at any point in time.
When equilibrium is attained, the reaction quotient is equal to the equilibrium constant.

In an equilibrium reaction for which $\Delta G^{\circ}$ = 0. Determine the value of equilibrium constant K. $\delta G$ =0

chemistry chemical equilibrium relationship between equilibrium constant, reaction quotient and gibbs energy law of mass action chemical equilibrium and acids-bases

  1. 1.0

  2. 2.7

  3. 7.6

  4. 8.5

Show answer
Correct Option: A
Explanation:

$\triangle G=-RTlnK\ If\quad \triangle G=0,E=0,Q=K\ No\quad reaction\quad takes\quad place$

$K {c}$ for an equilibrium $SO _{3}\rightleftharpoons SO _{2}(g)+ \frac{1}{2}O _{2}(g)$ is equal to 0.15 at 900 K. The equilibrium constant for the equation $2SO _{2}+ O _{2}\rightleftharpoons 2SO _{3}(g)$ is ___________.

chemistry chemical equilibrium relationship between equilibrium constant, reaction quotient and gibbs energy law of mass action chemical equilibrium and acids-bases

  1. $6.66$

  2. $44.4$

  3. $2.25$

  4. $0.44$

Show answer
Correct Option: B
Explanation:

$K _{c}$ for $SO _{3}\rightleftharpoons  SO _{2}+ \frac{1}{2} O _{2}$ is 0.15.

$K _{c}$ for the following reaction $ 2SO _{2}+ O _{2}\rightleftharpoons 2SO _{3}$ will be the reciprocal of square of the above equilibrium as stoichiometric coefficients are doubled and the reaction is reversed.

$K^{1} _{c} = \dfrac{1}{K^{2} _{c}} = \dfrac{1}{0.15^{2}} = 44.4$

The correct relationship between free energy change in a reaction and the corresponding equilibrium constant $K$ is:

chemistry chemical equilibrium relationship between equilibrium constant, reaction quotient and gibbs energy law of mass action chemical equilibrium and acids-bases

  1. $-\Delta G^{\circ}\, =\, RT\, in \, K$

  2. $\Delta G\, =\, RT\, in\, K$

  3. $-\, \Delta G \, =\, RT\, in\, K$

  4. $\Delta G^{\circ}\, =\, RT\, in\, K$

Show answer
Correct Option: A
Explanation:

The equilibrium constant is related to the free energy change of the reaction by the expression:

$K = e^{(-\Delta G^o/RT)}$ or $ln K = - \Delta G^o/RT$

or  $- \Delta G^o= RT \ ln K$ in which $T$ is the temperature in Kelvin and $R$ is the gas constant (1.986 cal/K mol)

Calculate value of $'ln(K _{eq})$' for the reaction at 250 K.
$N _2O _4 (g) \rightleftharpoons 2NO _2 (g)$
Given: $H^0 _f((NO _2)g) = + 40.407 kJ / mol$
$H^0 _f((N _2O _4)g) = + 70 kJ / mol$
$S^0 _r = 10 JK^{-1}$

chemistry chemical equilibrium relationship between equilibrium constant, reaction quotient and gibbs energy law of mass action chemical equilibrium and acids-bases

  1. 4

  2. -4

  3. 1.2

  4. -1.2

Show answer
Correct Option: B
Explanation:

$+G^0 = +H^0 -TS^0$
$+H _r^0 = (+ H _f^0)p - ( + H _f^0) _R$
$= 2 \times (+ 40.407) - (+70)$
$= + 10.814 kJ$
$+G^0 = + 10.814 kJ - 250 \times 10 J/K$
$= + 10.814 kJ - 2500 J = 8314 J$
$+G^0 = -RT ln K$
$8314 = - 8.314 \times 250 ln K$
$ln K = - 4.$

Assertion: For every chemical reaction at equilibrium, the standard Gibbs energy of reaction is zero.
Reason: At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs energy.

chemistry chemical equilibrium relationship between equilibrium constant, reaction quotient and gibbs energy law of mass action chemical equilibrium and acids-bases

  1. The Assertion is True, Reason is True; Reason is the correct explanation for Assertion

  2. The Assertion is True, Reason is True; Reason is NOT a correct explanation for Assertion

  3. The Assertion is True, Reason is False

  4. The Assertion is False, Reason is True

Show answer
Correct Option: D
Explanation:


The standard Gibb's energy for a reaction is given by $\Delta G^o$.

At equilibrium, $\Delta \mathrm{G}=0$ whereas $\ \Delta \mathrm{G}^{\mathrm{o}}$ for a reaction may or may not be zero.
For a spontaneous process, Gibb's energy for a reaction is always negative, $\Delta \mathrm{G}<0$
Hence, Assertion is false but Reason is true.

The correct relationship between free energy change in a reaction and the corresponding equilibrium constant, $K$ is:

chemistry chemical equilibrium relationship between equilibrium constant, reaction quotient and gibbs energy law of mass action chemical equilibrium and acids-bases

  1. $\Delta G^{o} = -RT ln K$

  2. $\Delta G = RT ln K$

  3. $\Delta G = -RT ln K$

  4. $\Delta G^{o} = RT ln K$

Show answer
Correct Option: A
Explanation:

The correct relationship between free energy change $\Delta G^{o}$ in a reaction and the corresponding equilibrium constant $K$ is $\Delta G^{o} = -RT :ln K$.

Here, $R$ is the ideal gas constant and $T$ is the temperature.

The value of equilibrium constant $(K _f)$ for the reaction: $Zn^{2+}(aq)+4OH^{-}(aq)\rightleftharpoons Zn(OH) _{4}^{2-}(aq)$ is represented in scientific notation as $p\times10^{q},$ then q is:
Given : $Zn^{2+}(aq)+2e^{-}\rightarrow Zn(s);  E^{0}=-0.76 V$
            $Zn(OH) _{4}^{2-}(aq)+2e^{-}\rightarrow Zn(s)+4OH^{-}(aq);  E^{0}=-1.36V$
            $2.303\dfrac{RT}{F}=0.06$

chemistry chemical equilibrium relationship between equilibrium constant, reaction quotient and gibbs energy law of mass action chemical equilibrium and acids-bases

  1. 20

  2. 10

  3. 15

  4. 21

Show answer
Correct Option: A
Explanation:

$\Delta G^o=-RTlnK _{eq} $

$logK _{eq}=\dfrac{nFE^{o}}{RT\times 2.303}\Rightarrow \dfrac{2\times 0.6}{0.06}\Rightarrow 20$

$K=10^{20}$


Greenhouse gas $CO _2$ can be converted to $CO(g)$ by the following reaction

$CO _2(g)+H _2(g)\rightarrow CO(g)+H _2O(g)$,
 
termed as water gas reaction.

The Equilibrium constant $K _p$ for the water gas reaction at $1000\;K$ is: 

 $(\Delta H _{\displaystyle1000\;K}=35040\;J\;mol^{-1}\ ; \Delta S _{1000\;K}=32.11\;J\;mol^{-1}\ K^{-1})$

(Note : The gases behave ideally).

chemistry chemical equilibrium relationship between equilibrium constant, reaction quotient and gibbs energy law of mass action chemical equilibrium and acids-bases

  1. $K _p=0.7030$

  2. $K _p=0.7300$

  3. $K _p=0.7330$

  4. $K _p=0.7303$

Show answer
Correct Option: A