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Standard XII

Chemistry

Properties of Water

The standard ...

Question

The standard potential of the following cells is 0.23 V at 15 $^{o}$ C and 0.21 V at 35 $^{o}$ C.

$P t | H_{2} (g) | H C l (a q) | A g C l (s) | A g (s)$

The solubility of $A g C l$ in water 25 $^{o}$ C.

[Note : The standard reduction potential of the $A g^{+} (a q) / A g (s)$ couple is 0.80 V at 25 $^{o}$ C]

1.215 \times 10^{- 5}

mol litre

^{- 1}

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4.415 \times 10^{- 5}

mol litre

^{- 1}

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2.345 \times 10^{- 5}

mol litre

^{- 1}

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None of these

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Solution

The correct option is A $1.215 \times 10^{- 5}$ mol litre $^{- 1}$
$P t_{H_{2}} (g) | H C l (a q) | A g C l_{s} | A g (s)$
(i) $\frac{1}{2} H_{2} \to H^{+} + e A n o d e$

$A g C l + e \to A g + C l^{-} C a t h o d e$
------------------------------------------------------
$\frac{1}{2} H_{2} + A g C l \to H^{+} + A g + C l^{-}$
(ii) $- Δ G^{o} = n E^{o} G = 1 \times 0.23 \times 96500 = 22195 J (a t 15^{o} C)$ ---------- (1)

$- Δ G^{o} = n E^{o} F = 1 \times 0.21 \times 96500 = 20265 J (a t 35^{o} C)$ ----------- (2)
Also,
$Δ G^{o} = Δ H^{o} - T Δ S^{o}$

Solving (1) and (2) equation we have
$- 22195 = Δ H^{o} - 288 \times Δ S^{o}$
$- 20265 = Δ H^{o} - 308 \times Δ S^{o}$
- - -
------------------------------------------------------------
$\Rightarrow Δ S^{o} = - 96.50 J$
Again, using (1) equation
$- 22195 = Δ H^{o} - 288 \times (- 96.5)$
$\Rightarrow Δ H = - 49987 J$
$∴ Δ H^{o} = - 49.987 k J$

At 298K or $25^{0} C$
$Δ G^{o} = Δ H^{o} - T Δ S^{o} = (- 49987) - 298 \times (- 96.5)$
$Δ G^{o} = - 21230 J = - n E^{0} F = - 1 \times E^{0} \times 96500$
$\Rightarrow E^{0} = 0.22 V$

Consider the following reaction at AgCl(s)/Ag electrode
$A g \to A g^{+} + e; E_{O P}^{o} = - 0.8 V$
$A g C l (s) + e \to A g + C l^{-}; E_{R P_{C l^{-} / A g C l / A g}}^{o} = 0.22 V$
--------------------------------------
Net : $A g C l \to A g^{+} + C l^{-}$
$∴ E_{c e l l} = E_{O P_{A g / A g^{+}}}^{o} - \frac{0.059}{1} l o g [A g^{+}] + E_{R P_{C l^{-} / A g C l / A g}}^{o} + \frac{0.059}{1} l o g \frac{1}{[C l^{-}]}$
$E_{c e l l} = 0$ at equilibrium
$\Rightarrow E_{O P_{A g / A g^{+}}}^{o} + E_{R P_{C l^{-} / A g C l / A g}}^{o} = \frac{0.059}{1} l o g [A g^{+}] [C l^{-}] = \frac{0.059}{1} l o g K_{s p}$
$\Rightarrow - 0.8 + 0.22 = \frac{0.059}{1} l o g K_{s p}$

$\Rightarrow l o g K_{s p} = \frac{- 0.58}{0.059} = - 9.83$
$\Rightarrow K_{s p_{A g C l}} = 1.477 \times 10^{- 10}$
$∴$ Solubility of $A g C l = \sqrt{(K_{s p})} = \sqrt{(1.477 \times 10^{- 10})} = 1.215 \times 10^{- 5}$ mol litre $^{- 1}$

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Similar questions

The standard potential of the following cells is 0.23 V at 15

^{o}

C and 0.21 V at 35

^{o}

P t, {H_{2}}_{(g)} | H C l_{(a q)} | | A g C l_{(S)} | A g_{(S)}

The cell reaction is :

The standard potential of the following cells is 0.23 V at 15

^{o}

C and 0.21 V at 35

^{o}

P t | H_{2} (g) | H C l (a q) | A g C l (s) | A g (s)

Calculate

- Δ H^{o}

(in kJ) for the cell reaction by assuming that these quantities remain unchanged in the range 15

^{o}

C to 35

^{o}

C( to the nearest integer)

Q. The standard potential of the following cell is

0.23 V

15^{\circ} C

and

0.21 V

25^{\circ} C

P t H_{2} (g) | H C l (a q .) | | A g C l (s) | A g (s)

(i) Write cell reaction.
(ii) Calculate

△ H^{\circ}

and

△ S^{\circ}

for the cell reaction by assuming that these quantities remain unchanged in the range

15^{\circ} C

35^{\circ} C

.
(iii) Calculate the solubility of

A g C l

in water at

25^{\circ} C

. Given the standard reduction potential of the

A g^{+} / A g

couple is

0.80 v o l t

25^{\circ} C

Q. The standard half cell reduction potential for

{A g}^{+} | A g

0.7991 V

25^{o} C

. Given that the experimental value of

K_{s p} = 1.56 \times 10^{- 10}

for

A g C l

, calculate the standard half cell reduction potential for the

A g | A g C l

electrode.

Q. The standard reduction potential of

A g^{+} | A g

electrode is

0.80 v o l t

. Calculate the standard electrode potential of

C l^{-} | A g C l | A g

25^{\circ} C

. Given solubility product,

K_{s p} (A g C l) = 1.8 \times 10^{- 10}

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The standard potential of the following cells is 0.23 V at 15oC and 0.21 V at 35oC. Pt|H2(g)|HCl(aq)|AgCl(s)|Ag(s)The solubility of AgCl in water 25oC. [Note : The standard reduction potential of the Ag+(aq)/Ag(s) couple is 0.80 V at 25oC]