Write the Nernst equation and calculate emf of the following cell at 298 K: Cr | Cr^3+(0 · 1 M ) ∥ Fe^2+(0 · 01 M )| Fe Given: E_Cr^3+ / Cr^ =-0.75 V…

\[\begin{aligned} E_{\text {cell }} & =E_{\text {cell }}^{0}-\frac{0.059}{6} \log \frac{\left[\mathrm{Cr}^{3+}\right]^{2}}{\left[\mathrm{Fe}^{2+}\right]^{3}} \\ E_{\text {cell }}^{0} & =-0.45-(-0.75) \\ & =0.30 \mathrm{~V} \\ E_{\text {cell }} & =0.3-\frac{0.059}{6} \log \frac{(0.1)^{2}}{(0.01)^{3}} \end{aligned} \] \(\displaystyle =0 \cdot 3-.00985 \log \frac{\left(10^{-1}\right)^{2}}{\left(10^{-2}\right)^{3}}\) \(\displaystyle =0 \cdot 3-.00985 \times 4 \log 10\) \(\displaystyle =0.3-0.0394\) \(\displaystyle =0 \cdot 2606 \mathrm{~V}\)