The diffusion coefficient of $T i$ is $2.0 imes 10^{-5} \mathrm{~cm}^{2} \mathrm{~s}^{-1}$ and that for $C d^{2+}$ is $0.72 imes 10^{-5} \mathrm{~cm}^{2} \mathrm{~s}^{-1}$. If a $1 \mathrm{mM}$ solution of $\mathrm{Cd}^{2+}$ gives a diffusion current of $8.15 \mu \mathrm{A}$, what will be the diffusion current for a $1 \mathrm{mM}$ solution of $T i^{+}$using the same polarographic cell?

Question

The diffusion coefficient of $T i$ is $2.0 	imes 10^{-5} \mathrm{~cm}^{2} \mathrm{~s}^{-1}$ and that for $C d^{2+}$ is $0.72 	imes 10^{-5} \mathrm{~cm}^{2} \mathrm{~s}^{-1}$. If a $1 \mathrm{mM}$ solution of $\mathrm{Cd}^{2+}$ gives a diffusion current of $8.15 \mu \mathrm{A}$, what will be the diffusion current for a $1 \mathrm{mM}$ solution of $T i^{+}$using the same polarographic cell?

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Identify the given data**: The diffusion coefficient of $Ti^+$ is $2.0 imes 10^{-5} \, ext{cm}^2 \, ext{s}^{-1}$ and that for $Cd^{2+}$ is $0.72 imes 10^{-5} \, ext{cm}^2 \, ext{s}^{-1}$. The diffusion current for a $1 \, ext{mM}$ solution of $Cd^{2+}$ is $8.15 \, \mu ext{A}$. ‖ ‖ 2 ⋮ **Use the Ilkovic equation**: The Ilkovic equation relates the diffusion current ($i_d$) to the diffusion coefficient ($D$), concentration ($C$), and other constants. The equation is $i_d = k \cdot n \cdot F \cdot D^{1/2} \cdot C$, where $k$ is a constant, $n$ is the number of electrons transferred, and $F$ is the Faraday constant. ‖ ‖ 3 ⋮ **Set up the ratio**: Since the same polarographic cell is used, $k$, $n$, and $F$ are constants and can be canceled out. The ratio of the diffusion currents for $Ti^+$ and $Cd^{2+}$ can be expressed as $\frac{i_{d, Ti^+}}{i_{d, Cd^{2+}}} = \frac{D_{Ti^+}^{1/2}}{D_{Cd^{2+}}^{1/2}}$. ‖ ‖ 4 ⋮ **Calculate the ratio**: Substitute the given diffusion coefficients into the ratio: $\frac{i_{d, Ti^+}}{8.15 \, \mu ext{A}} = \frac{(2.0 imes 10^{-5})^{1/2}}{(0.72 imes 10^{-5})^{1/2}}$. ‖ ‖ 5 ⋮ **Solve for $i_{d, Ti^+}$**: Calculate the square roots and solve for $i_{d, Ti^+}$: $\frac{i_{d, Ti^+}}{8.15 \, \mu ext{A}} = \frac{\sqrt{2.0 imes 10^{-5}}}{\sqrt{0.72 imes 10^{-5}}} = \frac{\sqrt{2.0}}{\sqrt{0.72}} \approx \frac{1.414}{0.848} \approx 1.67$. Therefore, $i_{d, Ti^+} = 8.15 \, \mu ext{A} imes 1.67 \approx 13.61 \, \mu ext{A}$. ‖ ∻Answer∻ ⚹ The diffusion current for a $1 \, ext{mM}$ solution of $Ti^+$ is approximately $13.61 \, \mu ext{A}$. ⚹ ∻Key Concept∻ ⚹ The Ilkovic equation relates diffusion current to the diffusion coefficient and concentration. ⚹ ∻Explanation∻ ⚹ By using the ratio of the diffusion coefficients and the given diffusion current for $Cd^{2+}$, we can calculate the diffusion current for $Ti^+$. ⚹◊What is the formula to calculate diffusion current in a polarographic cell?⍭ Generate me a similar question◊

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