Amixture of water and ethanol has a total mass of 100 kg. the
mole fraction of water is 0.752. what is the mass of ethanol in
this mixture, in kg?

45.8 kg

Explanation:

Given that the mole fraction of water = 0.752

For a binary system,

The mole fraction of water + The mole fraction of ethanol = 1

So,

The mole fraction of ethanol = 0.248

Given that the total mass = 100 kg

Let the mass of ethanol = x kg

The mass of water = 100 - x kg

The formula for the calculation of moles is shown below:

Molar mass of ethanol = 46.07 g/mol

Molar mass of water = 18 g/mol

Also, 1 g = 10⁻³ kg

So,

Molar mass of ethanol = 46 ×10⁻³ kg/mol

Molar mass of water = 18 ×10⁻³ kg/mol

Moles of ethanol = x / 46 ×10⁻³ moles

Moles of water = (100 - x) / 18 ×10⁻³ moles

So, according to definition of mole fraction:

Applying values as:

Solving for x, we get

x = 45.8 kg

Mass of ethanol in mixture = 45.8 kg