Equilibrium Constant from Nernst Equation

Q. For a cell involving one electron, $E_{cell}^0$ = 0.59 V at 298 K, the equilibrium constant for the cell reaction is:
[Given that $\frac{2.303RT}{F}$ = 0.059 V at T = 298 K]

1. $1.0\times {10}^2$
2. $1.0\times {10}^5$
3. $1.0\times {10}^{30}$
4. $1.0\times {10}^{10}$

Q. At ${100}^{o}C$ the $K_w$ of water is 55 times its value at ${25}^{o}C$. What will be the pH of neutral solution?
$(log55=1.74)$

1. 6.13
2. 7.00
3. 7.87
4. 5.13

Q. Calculate the equivalent conductivity of $1M{H}_{2}S{O}_4$ solution if its conductivity is $26\times {10}^{-2}oh{m}^{-1}c{m}^{-1}$.

$(\text{Atomic weight of sulphur}=32g/mol)$

1. ${\Lambda }_{eq}=2.6\times {10}^{2}oh{m}^{-1}c{m}^{2}equi{v}^{-1}$
2. ${\Lambda }_{eq}=1.3\times {10}^{2}oh{m}^{-1}c{m}^{2}equi{v}^{-1}$
3. ${\Lambda }_{eq}=13\times {10}^{-5}oh{m}^{-1}c{m}^{2}equi{v}^{-1}$
4. ${\Lambda }_{eq}=26\times {10}^{-5}oh{m}^{-1}c{m}^{2}equi{v}^{-1}$

Q. $E^{\circ }$ for the cell,
${\text{Zn(s)|Zn}}^{2+}\left(\text{aq}\right)||{\text{Cu}}^{2+}\text{(aq)|Cu(s)}$ is $1.10$ V at ${25}^{\circ }\text{C}$. The equilibrium constant for the reaction, $\text{Zn(s)}+{\text{Cu}}^{2+}\text{(aq)}\to \text{Cu(s)}+{\text{Zn}}^{2+}\text{(aq)}$ is $1.94\times {10}^x$. The value of $x$ is

1. $-23$
2. $37$
3. $18$
4. $13$

Q. In the acid-base titration
$[H_{3}P{O}_4\left(0.1M\right)+NaOH\left(0.1M\right)]$ , the e.m.f of the solution is measured by coupling this electrode with a suitable reference electrode. When an alkali is added, the pH of the solution is in accordance with the equation:
$E_{\text{cell}}=E_{\text{cell}}^{\circ }+0.059\text{pH}$
For $H_{3}P{O}_4:K{a}_1={10}^{-3},K{a}_2={10}^{-8},K{a}_3={10}^{-13}$
What is the e.m.f of the cell at the ${\text{II}}^{\text{nd}}$ end point of the titration if $E_{\text{cell}}^{\circ }$ at this stage is $1.3805\text{V}$

Q. EMF of hydrogen electrode in term of $pH$ at ${25}^{o}C$ is

1. $E_{H^{+}/H_2}=0.0591+pH$
2. $E_{H^{+}/H_2}=0.0591-pH$
3. $E_{H^{+}/H_2}=0.0591pH$
4. $E_{H^{+}/H_2}=-0.0591pH$

Q. For the cell reaction $2C{e}^{4+}+Co\to 2C{e}^{3+}+C{o}^{2+}$
$E_{cell}^o\text{is}1.89\text{V}$. $\text{If}{E}_{C{o}^{2+}|Co}^o\text{is}-0.28\text{V}$, What is the value of $E_{C{e}^{4+}|C{e}^{3+}}^o$

Q. . Fe3+(aq) + e– → Fe2+(aq), E° = +0.77 V Cl2(g) + 2e– → 2Cl–(aq), E° = +1.36 V Write the reaction which could be feasible using above half cells.

Q. The equilibrium constant $K_c$ for a reaction is 10. Calculate the value of change in standard Gibbs free energy $\Delta G^o\text{in}kJmo{l}^{-1}$ at 300 $K$.

1. 5.744
2. -5.744
3. -2.744
4. 2.744

Q. For a cell, $Cu\left(s\right)|C{u}^{2+}\left(0.001M\right)\parallel A{g}^{+}\left(0.01M\right)|Ag\left(s\right)$ the cell potential is found to be $0.43V$ at $298K$. The magnitude of standard electrode potential for $C{u}^{2+}$/Cu is _____ $\times {10}^{-2}V$.

[Given : $E_{A{g}^{+}/Ag}^{\ominus }=0.80V\text{and}\frac{2.303RT}{F}=0.06V$]

Q. The Gibbs energy for the decomposition of $A{l}_2{O}_3$ at $500$ ${}^{o}C$ is as follows:
$2/3A{l}_2{O}_3\to 4/3Al+O_2;{\Delta }_{r}G=+966$ kJ/mol.
The potential difference needed for electrolytic reduction of $A{l}_2{O}_3$ at ${500}^o$C is at least:

1. $5.0$V
2. $4.5$V
3. $3.0$V
4. $2.5$V

Q. What will be the $E^0$ value for the given half cell reaction?
$C{r}^{2+}\left(aq\right)+2e^{-}\to Cr\left(s\right)$
Given:
$E^0$ value for the half cell reaction,
$C{r}^{3+}\left(aq\right)+e^{-}\to C{r}^{2+}\left(aq\right);E^0=-0.41V$
$C{r}^{3+}\left(aq\right)+3e^{-}\to Cr\left(s\right);E^0=-0.74V$

1. $+0.33V$
2. $-1.15V$
3. $-0.33V$
4. $-0.91V$

Q. $E^{\circ }$ for the cell $Zn|Z{n}^{2+}\left(aq\right)||C{u}^{2+}\left(aq\right)|Cu\text{is}1.10V\text{at}{25}^{\circ }C$. The equilibrium constant for the reaction $Zn+C{u}^{2+}\left(aq\right)\rightleftharpoons Cu+Z{n}^{2+}$ is of the order of:

1. ${10}^{-28}$
2. ${10}^{37}$
3. ${10}^{18}$
4. ${10}^{17}$

Q.

$E^0$ for the cell, $Zn|Zn{{}^{2+}}_{\left(aq\right)}||Cu{{}^{2+}}_{\left(aq\right)}|Cu$ is $1.10V$ at ${25}^{0}C$. The equilibrium constant for $Zn+Cu{{}^{2+}}_{\left(aq\right)}\to Zn{{}^{2+}}_{\left(aq\right)}+Cu$ the cell reaction is of the order of :

1. ${10}^{-17}$
2. ${10}^{-37}$
3. ${10}^{37}$
4. ${10}^{17}$

Q. The $E_{cell}^0$ for the given cell reaction is $-0.32V$ at ${25}^{o}C$.
$Fe\left(s\right)+Z{n}^{2+}\left(aq\right)\rightleftharpoons Zn\left(s\right)+F{e}^{2+}\left(aq\right)$
What will be the value of $\log \left[F{e}^{2+}\right]$ at equilibrium when a piece of iron is placed in a $1M$ of $Z{n}^{2+}$ solution?

1. $-10.83$
2. $-5.42$
3. $+10.83$
4. $+5.42$

Q.

Q. De broglie equation derivation ?

Q. $E^{\circ }$ for the cell $Zn|Z{n}^{2+}\left(aq\right)||C{u}^{2+}\left(aq\right)|Cu)$ is $1.10v$ at ${25}^{\circ }$. The equilibrium constant for the reaction
$Zn+C{u}^{2+}\left(aq\right)\to Cu+Z{n}^{2+}\left(aq\right)$ is of the order of:

1. ${10}^{-28}$
2. ${10}^{37}$
3. ${10}^{18}$
4. ${10}^{17}$

Q. Calculate the equilibrium constant for the reaction, $2F{e}^{3+}+3I^{-}\rightleftharpoons 2F{e}^{2+}+I_3^{-}$. The standard reduction potentials in acidic conditions are $0.77$ and $0.54V$ respectively for $F{e}^{3+}|F{e}^{2+}$ and ${I_3}^{-}|I^{-}$ couples.

1. $7.26\times {10}^7$
2. $5.26\times {10}^7$
3. $6.04\times {10}^7$
4. $4.26\times {10}^7$

Q. The Gibbs' energy for the decomposition of $A{l}_2{O}_3$ at ${500}^{o}C$ is as follows:
$\frac{2}{3}A{l}_2{O}_3\to \frac{4}{3}Al+O_2;\Delta G=+966kJmo{l}^{-1}$.
The potential difference needed for the electrolytic reduction of aluminium oxide $\left(A{l}_2{O}_3\right)$ at ${500}^{o}C$ is at least:

1. 5 V
2. 3 V
3. 2.5 V
4. 4.5 V

Q. Use the following $E^o$ for the electrode potentials, calculate $\Delta G^o$ in $kJ$ for the indicated reaction.
$5C{e}^{4+}\left(aq\right)+M{n}^{2+}\left(aq\right)+4H_{2}O\left(l\right)\to Mn{O}_4^{-}\left(aq\right)+8H^{+}\left(aq\right)Mn{O}_4^{-}\left(aq\right)+5e^{-}\to M{n}^{2+}\left(aq\right)+4H_{2}O\left(l\right);E^o=+1.51VC{e}^{4+}+e^{-}\to C{e}^{3+}\left(aq\right);E^o=+1.61V$

1. $-9.65$
2. $-24.3$
3. $-48.25$
4. $-35.2$

Q. For a cell involving one electron, $E_{cell}^0$ = 0.59 V at 298 K, the equilibrium constant for the cell reaction is:
[Given that $\frac{2.303RT}{F}$ = 0.059 V at T = 298 K]

1. $1.0\times {10}^2$
2. $1.0\times {10}^5$
3. $1.0\times {10}^{10}$
4. $1.0\times {10}^{30}$

Q. EMF of the cell, $Ag|AgN{O}_3\left(0.1M\right)|KBr\left(1N\right),AgBr\left(s\right)|Ag$ is $-0.6\text{V}$ at $298\text{K}$
Calculate the $K_{sp}$ of $AgBr$ at $298\text{K}$.

1. $K_{sp}=4.0\times {10}^{-12}$
2. $K_{sp}=3.5\times {10}^{-12}$
3. $K_{sp}=4.8\times {10}^{-12}$
4. $K_{sp}=3.8\times {10}^{-12}$

Q. Which of the following statements is correct for a reversible process in a state of equilibrium?

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1. $\Delta G^o=2.303RT\log K$
2. $\Delta G^o=-2.303RT\log K$
3. $\Delta G=2.303RT\log K$
4. $\Delta G=-2.303RT\log K$

Q. Standard free energies of formation (in kJ/mol) at 298 K are -237.2, -394.4 and -8.2 for $H_{2}O\left(l\right),C{O}_2\left(g\right)$ and pentane (g), respectively. The value of $E_{cell}^0$ for the pentane-oxygen fuel cell is:

1. $1.0968V$
2. $0.0968V$
3. $1.968V$
4. $2.0968V$

Q. The emf of the cell $Zn|Z{n}^{2+}\left(0.1M\right)||F{e}^{2+}|Fe\left(0.01M\right)$ is $0.2905V$. Equilibrium constant for the cell reaction is

1. ${10}^{\frac{32}{0.591}}$
2. ${10}^{\frac{0.32}{0.0295}}$
3. ${10}^{\frac{0.26}{0.0295}}$
4. ${10}^{\frac{0.32}{0.295}}$

Q. The temperature coefficient of the EMF of the cell is given by:

1. $\frac{nF}{\Delta S}$
2. $\frac{\Delta S}{nF}$
3. $\frac{\Delta S}{nFT}$
4. $-nFE$

Q. $E^{\circ }$ for the electrochemical cell, $Zn\left(s\right)|Z{n}^{2+}1M(aq.)\parallel C{u}^{2+}1M(aq.)|Cu\left(s\right)$ is $1.10V$ at ${25}^{\circ }C$. The equilibrium constant for the cell reaction, $Zn\left(s\right)+C{u}^{2+}(aq.)\rightleftharpoons Z{n}^{2+}(aq.)+Cu\left(s\right)$ will be:

1. ${10}^{-39}$
2. ${10}^{39}$
3. ${10}^{-38}$
4. ${10}^{37}$

Q. $Zn|Z{n}^{2+}\left(C_1\right)||Z{n}^{2+}\left(C_2\right)|Zn$. For this cell $\Delta G$ is negative if:

1. $C_1=C_2$
2. $C_1>C_2$
3. $C_2>C_1$
4. None

Q. Consider the given reactions:

1. Reaction $\left(I\right)$ is faster than $\left(II\right)$
2. Reaction $\left(II\right)$ is faster than $\left(I\right)$
3. Reaction $\left(III\right)$ is faster than $\left(IV\right)$
4. Reaction $\left(IV\right)$ is faster than $\left(III\right)$