Question

The density of an equal-mass water 1 ethanol mixture is 0.913 g/cc at 20°C. If the density of water is 0.998 g/cm3 and ethanol is 0.789 g/cm3 with both at 20°C, does this equal-mass mixture possess a positive or negative excess volume at 20°C?

Answer 1

Answer:

Since water and ethanol have the same mass, there is an excess of positive volume at a temperature of 20°C

Explanation:

The component 1 refers to water and the component 2 refers to ethanol. The molar volume is

$V_{ethanol} =\frac{m_{ethanol} }{p_{ethanol} } =\frac{46.06}{0.789} =58.37cm^{3} /mol\\V_{water} =\frac{m_{water} }{p_{water} } =\frac{18}{0.998} =18.03cm^{3} /mol$

The excess volume is

$V_{E} =\frac{x_{1}m_{1}+x_{2}m_{2} }{p_{m} } -x_{1}V_{1} -x_{2} V_{2}$

Where xn are the mole fraction of water and ethanol, pm is the density of the mixture.

$V_{E} =\frac{(0.5*18)+(0.5*46.06)}{0.913} -(0.5*18.03)-(0.5*58.37)=55.3cm^{3}$

of the results, since water and ethanol have the same mass, there is an excess of positive volume at a temperature of 20°C