Chapter 5: Problem 7

Determine the reduction potential \(E_{\mathrm{Sn}^{4+} / \mathrm{sn}}^{\circ}\) if \(E_{\mathrm{Sn}^{2+} / \mathrm{Sn}}^{\circ}=-0.136 \mathrm{~V}\) and \(E_{\mathrm{Sn}^{4+} / \mathrm{sn}^{2+}}^{\circ}=0.15 \mathrm{~V}\). Also draw the corresponding Latimer diagram.

Short Answer

Expert verified

The standard reduction potential \(E_{\mathrm{Sn}^{4+} / \mathrm{Sn}}^{\circ}\) for the reaction where Sn is reduced from Sn4+ to Sn is 0.014 V. The Latimer diagram starts from Sn4+ reduced to Sn2+ with a potential of 0.15V, and then to Sn with a potential of -0.136V.

Step by step solution

Analyzing the given information

First, consider the provided reduction potentials. The standard reduction potential \(E_{\mathrm{Sn}^{2+} / \mathrm{Sn}}^{\circ}\) is the potential for the reduction of Sn2+ to Sn, while \(E_{\mathrm{Sn}^{4+} / \mathrm{Sn}^{2+}}^{\circ}\) is the potential for the reduction of Sn4+ to Sn2+. The value not given is the reduction potential \(E_{\mathrm{Sn}^{4+} / \mathrm{Sn}}^{\circ}\), which is the standard potential for the reduction of Sn4+ to Sn.

Calculating E( Sn4+ / Sn)

The reduction potential \(E_{\mathrm{Sn}^{4+} / \mathrm{Sn}}^{\circ}\) can be calculated using the given two potentials. This is because the reduction of Sn4+ to Sn (which is not provided) is equal to the reduction of Sn4+ to Sn2+ plus the reduction of Sn2+ to Sn (which are both provided in the task). In terms of the given potentials, this means: \(E_{\mathrm{Sn}^{4+} / \mathrm{Sn}}^{\circ} = E_{\mathrm{Sn}^{4+} / \mathrm{Sn}^{2+}}^{\circ} + E_{\mathrm{Sn}^{2+} / \mathrm{Sn}}^{\circ}\) Substituting the given values into this equation gives \(E_{\mathrm{Sn}^{4+} / \mathrm{Sn}}^{\circ} = 0.15V - 0.136V = 0.014V\).

Drawing the Latimer Diagram

The Latimer diagram represents a series of involved chemical species positioned in sequence of their redox states from most oxidized to most reduced. The potential difference between each pair denotes the reduction potential for the transformation from one species to another. The diagram starts with Sn4+ on the left, followed by Sn2+ with the reduction potential \(E_{\mathrm{Sn}^{4+} / \mathrm{Sn}^{2+}}^{\circ} = 0.15 V\), then Sn with the reduction potential of \(E_{\mathrm{Sn}^{2+} / \mathrm{Sn}}^{\circ} = -0.136 V\).

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Determine the reduction potential \(E_{\mathrm{Sn}^{4+} / \mathrm{sn}}^{\circ}\) if \(E_{\mathrm{Sn}^{2+} / \mathrm{Sn}}^{\circ}=-0.136 \mathrm{~V}\) and \(E_{\mathrm{Sn}^{4+} / \mathrm{sn}^{2+}}^{\circ}=0.15 \mathrm{~V}\). Also draw the corresponding Latimer diagram.

Short Answer

Step by step solution

Analyzing the given information

Calculating E( Sn4+ / Sn)

Drawing the Latimer Diagram

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