Answer
$$
\begin{aligned}
& E_{\text {Cell }}=\frac{R T}{n F} \ln (K) \\
& n F E=R T \ln (K) \\
& \frac{n F E}{R T}=\ln (K) \\
& K=e^{\frac{n F E}{R T}} \\
& n=3 e^{-}, F=96485 \mathrm{C} \mathrm{mol}^{-}, E=0.177 \mathrm{~V}, R=8.314 \mathrm{~J} \mathrm{~mol}^{-} \mathrm{K}^{-}, T=298 \mathrm{~K} \\
& K=e^{\frac{\left(3 e^{-}\right)(96485)(0.177)}{(8.314)(298)}} \\
& K=e^{20.679} \\
& K=9.57 \times 10^{8}
\end{aligned}
$$
Work Step by Step
What is given...
$$
\begin{aligned}
& E_{\text {Cell }}=0.177 \mathrm{~V} \\
& T=298 \mathrm{~K} \\
& n=3
\end{aligned}
$$
Formula...
$$
\begin{aligned}
& E_{\text {Cell }}=\frac{R T}{n F} \ln (K) \\
& n F E=R T \ln (K) \\
& \frac{n F E}{R T}=\ln (K) \\
& K=e^{\frac{n F E}{R T}} \\
& n=3 e^{-}, F=96485 \mathrm{C} \mathrm{mol}^{-}, E=0.177 \mathrm{~V}, R=8.314 \mathrm{~J} \mathrm{~mol}^{-} \mathrm{K}^{-}, T=298 \mathrm{~K} \\
& K=e^{\frac{\left(3 e^{-}\right)(96485)(0.177)}{(8.314)(298)}} \\
& K=e^{20.679} \\
& K=9.57 \times 10^{8}
\end{aligned}
$$
