Antifreeze is used in automobile radiators to keep the coolant from freezing. In geographical areas where winter temperatures go below the freezing point of water, using pure water as the coolant could allow the water to freeze. Since water expands when it freezes, freezing coolant could crack engine blocks, radiators, and coolant lines. The main component in antifreeze is ethylene glycol.

Question

What is the concentration of ethylene glycol in a solution of water, in molality (m), if the freezing point dropped by 2.64oC'>2.64oC (ΔTf.) Kf for ethylene glycol is 1.86 oC/m

m (round to 3 sig figs)

Answer 1

To calculate the molality (m) of ethylene glycol in the solution, we can use the formula for freezing point depression:

\[ \Delta T_f = K_f \cdot m \]

Where:

• \(\Delta T_f\) is the change in freezing point (in °C),
• \(K_f\) is the freezing point depression constant for the solvent (in °C/m),
• \(m\) is the molality (in mol/kg).

Given:

• \(\Delta T_f = 2.64 ,°C\)
• \(K_f = 1.86 ,°C/m\)

We can rearrange the equation to solve for molality (m):

\[ m = \frac{\Delta T_f}{K_f} \]

Now, we can substitute the given values into the formula:

\[ m = \frac{2.64 ,°C}{1.86 ,°C/m} \]

Calculating this gives:

\[ m \approx 1.4193548387 , m \]

Rounding to three significant figures, we get:

\[ m \approx 1.42 , m \]

Therefore, the concentration of ethylene glycol in the solution of water is approximately 1.42 mol/kg.