A galvanic cell is composed of a standard $Z n$ electrode and a chromium electrode immersed in a solution containing ${C r}^{3 +}$ . At what concentration of ${C r}^{3 +}$ will the emf of the cell be zero?

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Solution

Let at concentration $x$ M of ${C r}^{3 +}$ , $ε_{c e l l} = 0$

$ε_{c e l l} = ε_{c e l l}^{o} = \frac{0.0592}{6} log \frac{{[{Z n}^{2 +}]}^{3}}{{[{C r}^{3 +}]}^{2}}$

$0 = (ε_{{C r}^{3 +} / C r}^{0} - ε_{{Z n}^{2 +} / Z n}^{0}) - \frac{0.0592}{6} log \frac{{[1]}^{3}}{{[x]}^{2}}$

$= {- 0.74 - (- 0.76)} + \frac{0.0592}{6} log {[x]}^{2} \Rightarrow - 0.02 = \frac{0.0592}{6} \times log x$

$log x = \frac{- 0.06}{0.0592} = - 1 \Rightarrow x = 10^{- 1} = 0.1 M$

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A galvanic cell is composed of a standard Zn electrode and a chromium electrode immersed in a solution containing Cr3+. At what concentration of Cr3+ will the emf of the cell be zero?

Let at concentration xM of Cr3+, εcell=0εcell=εocell=0.05926log[Zn2+]3[Cr3+]20=(ε0Cr3+/Cr−ε0Zn2+/Zn)−0.05926log[1]3[x]2={−0.74−(−0.76)}+0.05926log[x]2⇒−0.02=0.05926×logxlogx=−0.060.0592=−1⇒x=10−1=0.1M

A galvanic cell is composed of a standard $Z n$ electrode and a chromium electrode immersed in a solution containing ${C r}^{3 +}$ . At what concentration of ${C r}^{3 +}$ will the emf of the cell be zero?