For the electrochemical cell, Mg(s) Mg 2+ aq,1 M Cu 2+ aq,1 M Cu s the standard emf of the cell is 2 .70 V at 300 K . When the concentration of Mg 2+ is changed to x M, the cell potential changes to 2 .67 V at 300 K . The value of x is ____

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For the electrochemical cell, Mg(s) Mg 2+ aq,1 M Cu 2+ aq,1 M Cu s the standard emf of the cell is 2 .70 V at 300 K . When the concentration of Mg 2+ is changed to x M, the cell potential changes to 2 .67 V at 300 K . The value of x is ________. (given, F R =11500 K V − 1 , where F is the Faraday constant and R is the gas constants, ln 10 = 2 .30 )

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Mg s + Cu 2+ aq → Mg 2+ aq + Cu s E cell o = 2 .70, E cell = 2 .67, Mg 2+ = xM, Cu 2+ = 1 M E cell = E cell o − RT nF ln x 2 .67 = 2 .70 − RT 2F ln x − 0 .03 = − R × 300 2F × ln x ln x = 0 .03 × 2 300 × F R = 0 .03 × 2 × 11500 300 × 1 ln x = 2 .30 = ln 10 x = 10

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