A pH glass/calomel electrode was found to develop a potential of -0.0390 V when used with buffer of pH 5.52. With an unknown solution, the potential was -0.360 V. Calculate the pH of the unknown solution

To calculate the pH of the unknown solution, we can use the Nernst equation. The Nernst equation relates the measured potential of an electrode to the concentration of the species being measured.

The Nernst equation is given by:

E = E° - (RT / nF) * ln(Q)

Where:
E is the measured potential
E° is the standard potential
R is the gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
n is the number of electrons transferred in the redox reaction
F is the Faraday constant (96485 C/mol)
Q is the reaction quotient

In our case, we are measuring the potential of a pH electrode, which is related to the hydrogen ion concentration. The redox reaction occurs between the hydrogen ions and the reference electrode, which is either a calomel or a pH glass electrode.

The standard potential for a pH electrode is 0.00 V. Therefore, we can rewrite the Nernst equation as:

E = - (RT / nF) * ln(Q)

By rearranging the equation and solving for Q, we get:

Q = exp((E / -(RT / nF)))

Now, let's plug in the given values:

E = -0.360 V
T = 298 K (room temperature)
n = 1 (since it's a proton transfer reaction)
F = 96485 C/mol

Q = exp((-0.360 / (-(8.314 J/(mol·K)) * 298 K / 1 * 96485 C/mol)))

Calculating the value of Q using the given formula, we find:

Q = exp(1.42742)

Taking the exponential of 1.42742, we get:

Q ≈ 4.165

Now that we have the value of Q, we can use it to find the pH. The pH is related to the hydrogen ion concentration (H+) by the equation:

pH = -log10([H+])

Since we know that the pH is 5.52 when the potential is -0.0390 V (the buffer solution), we can set up the equation:

5.52 = -log10([H+])

Taking the logarithm of both sides, we get:

[H+] = 10^(-5.52)

Calculating the value of [H+], we find:

[H+] ≈ 2.91 * 10^(-6) M

Now, we can find the pH of the unknown solution using the calculated Q and the hydrogen ion concentration ([H+]):

pH = -log10([H+])
= -log10(4.165 * 10^(-6))
≈ 5.38

Therefore, the pH of the unknown solution is approximately 5.38.