Question

A solution is made up of 220.7 g of ethanol and 130.8 g of H2O.

If the volume of the solution is 403.4 cm3 and the partial molar volume of H2O is 17.0 cm3, what is the partial molar volume of ethanol under these conditions?

Answer 1

Number of moles,n = mass/molar mass

Number of moles of H2O,n_water= 130.8g/18.02g/mol = 7.2586mol

Number of moles of ethanol,n_ethanol = 220.7g/46.07g/mol = 4.7905mol

Partial molar volume of water ,V_water = 17.0cm³

Volume of solution,V_{solution = 403.4cm}³

V_solution =( n_ethanol× V_ethanol ) + ( n_water × V_water  )

403.4cm³ = (4.7905mol × V_ethanol ) + ( 7.2586mol × 17.0cm³/mol)

403.4cm³ = (4.7905mol × V_ethanol ) + 123.396 cm³

4.7905mol × V_ethanol = 280.004cm³

  V_ethanol = 58.4 cm³/mol

Therefore

Partial molar volume of ethanol = 58.4 cm³/mol