The pH of the unknown solution is 3.07.
Step-by-step explanation:
1.Find the cell potential as a function of pH
From the Nernst Equation:
Ecell=E∘cell−RT /zF × lnQ
where
R denotes the Universal Gas Constant
T denotes the temperature
z denotes the moles of electrons transferred per mole of hydrogen
F denotes the Faraday constant
Q denotes the reaction quotient
Substitute the values,
E∘cell=0 lnQ=2.303logQ
E0cell=−2.30/RT /zF × log Q
Solving the equation,
2. Find the Q value
Q=[H+]2prod pH₂, product/ [H+]2reactpH₂, reactant
Q=[H+]^2×1/1×1=[H+]2
Taking the log
logQ= log[H+]^2=2log[H+]=-2pH
From the formula,
Ecell=−2.303RT /zF× logQ
E cell= 2.303 × 8.314 CK mol (inverse) × 298.15
K × 2pH /2×96 485 C⋅mol
( inverse)
E cell= 0.0592 V × pH
3. Finding the pH value
E cell= 0.0592 V × pH
pH = E cell/ 0.0592 V= 0.182V/ 0.0592V
pH=3.07
The pH of the unknown solution is 3.07.