# Nernst equation

Here is the question:

Q: Show with the aid of a form of the Nernst equation that when using a pH sensitive glass electrode and reference electrode that the measured potential is proportional to pH.

This is the answer I have:

Nernst equation:

E = E ° - 0.059/n * log Q

Q is the reaction quotient, active mass of products divided by active mass of reactants.

The glass electrode half reaction can be written as

H2 -----> 2H(+) + 2e(-)

Substituting in the Nernst equation we have

E = E° - 0.059/2 * log [H+]2 / [H2]

At constant H2, also we know E° is zero. So,

E = -0.059/2 * log [H+]2

E = -0.059 * log [H+]

E = 0.059 * pH

Thus, E is directly proportional to the pH of the solution, as -log[H+] is defined to be pH

Is this correct? How is E = E ° - 0.059/n * log Q deduced from E = E ° - (RT/nF)lnQ

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How is E = E ° - 0.059/n * log Q deduced from E = E ° - (RT/nF)lnQ

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This solution examines a problem solved using the Nernst equation and assesses its accuracy.