Question

Describe how you could experimentally determine the volume of mixing V mix in a 0.95 mole fraction A and 0.05 mole fraction B

Answer 1

Volume of mixing, V_mix = n_AV_A' + n_BV_B'

n = mole fraction, V' = partial volume = (V₂ - V₁/n_A,2 - n_A,1)_{per 1 mol of B}

You have the mole fraction of A and B, what you need is the partial volume of the components at the experimental temperature.

To determine the partial volume, we have to measure the density of the solution at two concentrations, one at the concentration below 0.95 mole fraction A (let it be d₁, at 0.92 mole fraction of A) and another at the concentration above 0.95 mole fraction A (let it be d₂, at 0.98 mole fraction of A).

Now, if you have the molar mass of A and B, you can calculate the mass of A per 1 mole of B in the first solution. Once you have the mass of A (per 1 mole of B) you can calculate the volume of this A by dividing the mass by the density (d₁).

Similarly you can calculate the mass of A per 1 mole of B in the second solution then calculate the volume of this A by dividing the mass by the density (d₂).

Plug this equation in (V₂ - V₁/n_A,2 - n_A,1)_{per 1 mol of B} to calculate V_A' in this range.

Similarly determine V_B'.

Calculate Volume of mixing, V_mix = n_AV_A' + n_BV_B' by putting the values of partial volumes and n_A = 0.95 , n_B = 0.05.