Answer to Question #130230 in General Chemistry for Triumph

Question

A divalent element x has a specific heat of 0.106 cal/g/°C. When a solution of the sulphate of x is electrolysed, 4.85g of x is deposited at the cathode and one litre of oxygen gas, measured at 16°C and 743mmHg pressure is evolved at the anode. Calculate the relative atomic mass of x (molar heat capacity =6.4 cal/mol/°C)

Answer 1

Ideal gas low:

PV=nRT

Molar gas constant

R=0.082058 L×atm/(K×mol)

T = 16 + 273.15 = 289.15 K

P = 0.977 atm

n(O₂) = PV/RT

n(O₂) = 0.977×1/0.082058×289.15 = 0.041 mol

Electrolysis reaction:

2XSO₄ + 2H₂O → 2X + 2H₂SO₄ + O₂

n(X) = 2n(O₂)

n(X) = 2×0.041 = 0.082 mol

M = m/n

M(X) = 4.85/0.082 = 59.14 g/mol

Answer: 59.14 g/mol