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Calculate E and Ag for the Following at 28°C - Chemistry

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Numerical

Calculate Ecell and ΔG for the following at 28°C :

Mg(s) + Sn2+( 0.04M ) → Mg2+( 0.06M ) + Sn(s)

cell = 2.23V. Is the reaction spontaneous ?

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Solution

`Mg_(s) + Sn_(aq)^(2+) -> Mg_(aq)^(2+) + Sn_(s)`

`[Sn^(2+)] = 0.04M[Mg^(2+)] = 0.06M`

Q = `[Mg^(2+)]/[Sn^(2+)] = [0.06]/[0.04] = 1.5`

`E_(cell)^(°) = 2.23V`

R = 8.314 JK-1 mol-1
T = 28°C = 28 + 273 = 301K
n = 2
F = 96500 C/mol e-

∴ `E_(cell) = E_(cell)^(°) - [2.303 RT]/[nF] log_10 Q`

= `2.23 - [2.303 xx 8.314 xx 301]/[2 xx 96500] log_10 (1.5)`

= `2.23 - [2.303 xx 8.314 xx 301]/[2 xx 96500] xx (0.1760)`

= 2.23 - 0.005255

`E_(cell)` = -2.2247 V
ΔG = `nFE_(cell)`

ΔG = `-2 xx 96500 xx 2.2247`

ΔG = - 429367 J
∵ ΔG is negative therefore reaction is spontaneous.

Concept: Galvanic Cells - Introduction
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