Question

A solution is made up of 184 g of ethanol, CH3CH2OH, and 108 g of water. If the volume of the solution is 334 cm3 and the partial molar volume of water is 17 cm3 mol-1 , what is the partial molar volume of ethanol under these conditions?

Answer 1

At constant temperature and pressure; Euler,s theorem
the total volume of solution V = V_A.n_A + V_B.n_B
Where, V_A and V_B are the partial molar volume of compound A and B.
n_A and n_B are the no. of moles of A and B.

We have Ethanol and water mixture.

no. moles of ethanol ne = mass/mol.wt
                       = 184 g/46.07 g·mol⁻¹
                       = 4.0 mol
no. moles of water nw = 108g/18.0153 g.mol^-1
                      = 6 mol
                  
Partial molar volume of water V_w = 17 cm³.mol^-1
total volume of the solution V = 334 cm³
Partial molar volume V_e =?

Therefore; V = V_w.n_w + V_e.n_e
334 cm³ = 17 cm³.mol^-1 x 6.0 mol + V_e x 4.0 mol
232 cm³ = V_e x 4.0 mol
V_e = 58 cm³.mol^-1

Hence, the partial molar volume of ethanol = 58 cm³.mol^-1