How to Get PH from a E Cell Value

To calculate the pH of a solution from the cell potential (E° cell) of an electrochemical cell, you can use the Nernst equation. Here’s how you can approach the problem:

1. Understand the Nernst Equation:

The Nernst equation relates the cell potential to the concentrations of the reactants and products, temperature, and the number of electrons transferred in the redox reaction.

E=E∘−0.0591nlog⁡[products][reactants]E = E^\circ – \frac{0.0591}{n} \log \frac{[ \text{products} ]}{[ \text{reactants} ]}E=E∘−n0.0591​log[reactants][products]​

Where:

• $E$ is the cell potential under non-standard conditions.
• E∘E^\circE∘ is the standard cell potential.
• $n$ is the number of moles of electrons transferred in the reaction.
• $[\text{products}]/[\text{reactants}]$ is the reaction quotient.

2. Set Up the Cell Reaction:

Identify the half-reactions and overall cell reaction. For example, in a cell involving hydrogen (like a hydrogen electrode), the relevant half-reaction is:

2H++2e−→H2(g)2H^+ + 2e^- \rightarrow H_2(g)2H++2e−→H2​(g)

3. Relate Cell Potential to pH:

If the cell involves the reduction of hydrogen ions, the reaction quotient can be related to the hydrogen ion concentration:

E=E∘−0.0591nlog⁡[H2][H+]2E = E^\circ – \frac{0.0591}{n} \log \frac{[H_2]}{[H^+]^2}E=E∘−n0.0591​log[H+]2[H2​]​

Simplifying for a hydrogen electrode (where E∘E^\circE∘ is 0 V and [H2][H_2][H2​] is constant at 1 atm):

E=−0.05912log⁡[H+]2E = – \frac{0.0591}{2} \log [H^+]^2E=−20.0591​log[H+]2

Since pH=−log⁡[H+]\text{pH} = -\log[H^+]pH=−log[H+]:

$$E=-0.0591\times \text{pH}$$

Therefore:

pH=−E0.0591\text{pH} = \frac{-E}{0.0591}pH=0.0591−E​

4. Calculate the pH:

Plug in the value of the cell potential (E) measured under the specific conditions:

pH=−E0.0591\text{pH} = \frac{-E}{0.0591}pH=0.0591−E​

For example, if you measure a cell potential of 0.177 V (for a standard hydrogen electrode setup):

pH=−0.1770.0591≈3.0\text{pH} = \frac{-0.177}{0.0591} \approx 3.0pH=0.0591−0.177​≈3.0

This means the solution has a pH of approximately 3.0.

Summary:

• Determine the standard cell potential (E∘E^\circE∘) and the measured cell potential (E).
• Use the Nernst equation to relate the cell potential to the hydrogen ion concentration.
• Calculate the pH from the relation pH=−E0.0591\text{pH} = \frac{-E}{0.0591}pH=0.0591−E​.

This method applies primarily to electrochemical cells involving hydrogen ions, like a hydrogen electrode. For other systems, the exact relationship between cell potential and pH may differ depending on the half-reactions involved.

Share the Fun!