What is the pH of the unknown solution?
A voltaic cell is constructed in which the cathode is a standard hydrogen electrode and the anode is a hydrogen electrode (P(H2)= 1atm) immersed in a solution of unknown [H+]. If the cell potential is 0.177 V, what is the pH of the unknown solution at 298 K?
A voltaic cell is constructed in which the cathode is a standard hydrogen electrode and the anode is a hydrogen electrode (P(H2)= 1atm) immersed in a solution of unknown [H+]. If the cell potential is 0.177 V, what is the pH of the unknown solution at 298 K?
1 Answer
pH = 2.99
Explanation:
The cell diagram for your cell is
You have a hydrogen concentration cell.
The half-cell reactions are
Because the two half-reactions are identical,
Cell potential as a function of pH
The cell is not at standard conditions, so we must use the Nernst Equation:
#E_text(cell) = E_text(cell)^@ - (RT)/(zF)lnQ#
where
But
#color(blue)(bar(ul(|color(white)(a/a)E_text(cell) = - (2.303RT)/(zF)logQcolor(white)(a/a)|)))" "#
#color(blue)(bar(ul(|color(white)(a/a)E_text(cell) = "0.0592 V × pH"color(white)(a/a)|)))" "#
Calculate the pH