Ethylene glycol (EG), CH2(OH)CH2(OH), is a common automobile antifreeze. It is water soluble and fairly nonvolatile (b.p. 197°C). Calculate the freezing point of a solution containing 651 g of this substance in 2505 g of water. Would you keep this substance in your car radiator during the summer?

Question

Ethylene glycol (EG), [latex]CH_{2}(OH)CH_{2}(OH)[/latex] , is a common automobile antifreeze. It is water soluble and fairly nonvolatile (b.p. 197°C). Calculate the freezing point of a solution containing 651 g of this substance in 2505 g of water. Would you keep this substance in your car radiator during the summer? The molar mass of ethylene glycol is 62.01 g.

Strategy This question asks for the depression in freezing point of the solution.
The information given enables us to calculate the molality of the solution and we refer to Table 12.2 for the [latex]K_{f}[/latex] of water.

Accepted Answer

To solve for the molality of the solution, we need to know the number of moles of EG and the mass of the solvent in kilograms. We find the molar mass of EG, and convert the mass of the solvent to 2.505 kg, and calculate the molality as follows:

[latex]651 \cancel{g EG} imes \frac{1 mol EG}{62.07 \cancel{g EG}}=10.5 mol EG [/latex]

[latex]m=\frac{moles of solute}{mass of solvent (kg)} [/latex]

[latex]=\frac{10.5 mol EG}{2.505 kg H_{2}O }=4.19 mol EG/kg H_{2}O[/latex]

=4.19 m

From Equation (12.7) and Table 12.2 we write

Solvent	Normal Freezing Point (C)*	[latex]K_{f}[/latex] (C/m)	Normal Boiling Point (C)*	[latex]K_{B}[/latex] (C/m)
Water	0	1.86	100	0.52
Benzene	5.5	5.12	80.1	2.53
Ethanol	-117.3	1.99	78.4	1.22
Acetic acid	16.6	3.9	117.9	2.93
Cycolohexane	6.6	20	80.7	2.79

[latex]ΔT_{f}=K_{f}m[/latex]

=(1.86°C/m)(4.19 m)

=7.79°C

Because pure water freezes at 0°C, the solution will freeze at (0 − 7.79)°C or −7.79°C. We can calculate boiling-point elevation in the same way as follows:

[latex]ΔT_{b}=K_{b}m[/latex]

=(0.52°C/m)(4.19 m)

=2.2°C

Because the solution will boil at (100 + 2.2)°C, or 102.2°C, it would be preferable to leave the antifreeze in your car radiator in summer to prevent the solution from boiling.

Question 12.8: Ethylene glycol (EG), CH2(OH)CH2(OH), is a common automobile...

Related Answered Questions

Calculate the molality of a 35.4 percent (by mass) aqueous solution of phosphoric acid (H3PO4). The molar mass of phosphoric acid is 97.99 g. Strategy In solving this type of problem, it is convenient to assume that we start with 100.0 g of the solution. If the mass of phosphoric acid is 35.4 ...

Verified Answer:

The osmotic pressure of a 0.010 M potassium iodide (KI) solution at 25°C is 0.465 atm. Calculate the van’t Hoff factor for KI at this concentration. Strategy Note that KI is a strong electrolyte, so we expect it to dissociate completely in solution. If so, its osmotic pressure would be ...

Verified Answer:

Verified Answer:

A 7.85-g sample of a compound with the empirical formula C5H4 is dissolved in 301 g of benzene. The freezing point of the solution is 1.05°C below that of pure benzene. What are the molar mass and molecular formula of this compound? Strategy Solving this problem requires three steps. First, we ...

Verified Answer:

Verified Answer:

Verified Answer:

Verified Answer:

The density of a 2.45 M aqueous solution of methanol (CH3OH) is 0.976 g/mL. What is the molality of the solution? The molar mass of methanol is 32.04 g. Strategy To calculate the molality, we need to know the number of moles of methanol and the mass of solvent in kilograms. We assume 1 L of ...

Verified Answer:

Calculate the molality of a sulfuric acid solution containing 24.4 g of sulfuric acid in 198 g of water. The molar mass of sulfuric acid is 98.09 g. Strategy To calculate the molality of a solution, we need to know the number of moles of solute and the mass of the solvent in kilograms. ...

Verified Answer:

A sample of 0.892 g of potassium chloride (KCl) is dissolved in 54.6 g of water. What is the percent by mass of KCl in the solution? Strategy We are given the mass of a solute dissolved in a certain amount of solvent. Therefore, we can calculate the mass percent of KCl using Equation (12.1). ...

Verified Answer: