Question

In cars, ethylene glycol, C2H6O2, is used as a coolant and antifreeze. A mechanic fills a radiator with 7.1 kg of ethylene glycol and 1.2 kg of water.

What is the molar mass of ethylene glycol?
What is the molality of the water in the solution?

Answer 1

Answer: Molecular mass of ethylene glycol is 62 g/mol and molality of solution will be 9.39 mol/kg.

Step-by-step explanation:

• To calculate the molar mass of ethylene glycol, we add the mass of each element multiplied with their individual atoms.

Mass of oxygen atom = 16 g/mol

Mass of hydrogen atom = 1 g/mol

Mass of carbon atom = 12 g/mol

Mass of ethylene glycol =
`[(2* 12)+(6* 1)+(2* 16)]=62g/mol`

• Molality of the solution is defined as the ratio of moles of solute to the mass of solvent present in kilograms.

Mathematically,

`\text{Molality}=\frac{\text{Moles of solute}}{\text{Mass of solvent (in kg)}}=\frac{\text{Given mass of solute}}{\text{Molar mass of solute}* \text{Mass of solvent (in kg)}}`

Water is the solute and ethylene glycol is the solvent in this case.

We are given:

Mass of solute (water) = 1.2 kg = 1200 g (Conversion factor: 1 kg = 1000 g)

Molar mass of solute (water) = 18 g/mol

Mass of solvent (ethylene glycol) = 7.1 kg

Putting values in above equation, we get:

`\text{Molality}=(1200g)/(18g/mol* 7.1kg)=9.39mol/kg`

Hence, molecular mass of ethylene glycol is 62 g/mol and molality of solution will be 9.39 mol/kg.

Answer 2

Based on the given molecular formula, the molar mass of ethylene glycol is 62 g/mol. We solve for the number of moles of the solute,
n = (7.1 kg)(1000 g/ 1 kg) / 62g/mol = 114.52 mol
Then, we divide this value by the given mass of the water in kg
m = (114.52 mol) / 1.2 kg = 95.43 m
Thus, the molality of the substance is approximately equal to 95.43 m.