Tag: chemical equilibrium

Questions Related to chemical equilibrium

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. $0.44$

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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
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.

$\Delta G$ for the reaction at 1000 K is : 

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

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

  1. $2930\;J$

  2. $2934\;J$

  3. $2300\;J$

  4. None of these

Show answer
Correct Option: A
Explanation:

A.2930J
$\triangle G=\triangle H-T\triangle S\ \triangle G=35040-1000\times 32.11\ \quad \quad \quad \quad =35040-32110\ \quad \quad \quad \quad =2930J$

Steam undergoes decomposition at high temperature as per the reaction
$H _{2}O(g) \rightleftharpoons  H _{2}(g)+\frac{1}{2}O _{2}(g), \Delta H^{\circ}=200 kJ  mol^{-1} \Delta S^{\circ}=40  J  mol^{-1}$
The temperature at which equilibrium constant is unit is :

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

  1. 3000 Kelvin

  2. 5000 Kelvin

  3. 5333 Kelvin

  4. 5 Kelvin

Show answer
Correct Option: B
Explanation:

$\Delta G^{\circ}=\Delta H^{\circ}-T\Delta S^{\circ}=-RT  ln Keq = 0  [Keq = 1]$.
$\Rightarrow T=\frac{\Delta H^{\circ}}{\Delta S^{\circ}}=\frac{200\times 10^{3}}{40}=5000  K$