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26 November, 22:10

A concentration cell consisting of two hydrogen electrodes (PH2 = 1 atm), where the cathode is a standard hydrogen electrode and the anode solution has an unknown pH, has a cell voltage of 0.182 V. What is the pH in the unknown solution? Assume the temperature of the solutions is 298 K. pH =

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  1. 26 November, 22:34
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    The pH of the unknown solution is 3.07.

    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.
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