Magnesium chloride is often used to melt ice on sidewalks.Considering that the solubility of magnesium chloride (95.21 g/mol)in water is 54.3 g per 100.0 g of water,what is the lowest temperature that you would expect to be able to melt ice with magnesium chloride? Assume ideal behavior.[K_f(water)= 1.86 $\circ$ C/m]

Question

Quizplus · Accepted Answer

To calculate the lowest temperature at which magnesium chloride can melt ice, we need to use the freezing point depression formula:

ΔTf = Kf × molality

where ΔTf is the change in freezing point, Kf is the freezing point depression constant for the solvent (water), and molality is the concentration of solute (magnesium chloride) in terms of moles of solute per kilogram of solvent.

First, we need to calculate the molality of magnesium chloride in solution. We can do this by converting the given solubility from grams per 100 grams of water to moles per kilogram:

54.3 g MgCl2 / 100 g H2O × (1 mol MgCl2 / 95.21 g) / (0.100 kg H2O / 1000 g) = 5.72 mol/kg

Next, we can plug in the values for Kf and molality and solve for ΔTf:

ΔTf = (1.86°C/m) × 5.72 mol/kg = 10.64°C

Finally, we need to convert ΔTf from Celsius to Fahrenheit to get the answer:

ΔTf = 10.64°C × 1.8°F/°C ≈ 19.15°F

Since the freezing point depression is a lowering of the freezing point, we need to subtract ΔTf from the freezing point of pure water (32°F) to get the lowest temperature at which magnesium chloride can melt ice:

32°F - 19.15°F ≈ 12.85°F

Therefore, the best choice is B (-31.8°F) since it is the closest option to 12.85°F.

Magnesium Chloride Is Often Used to Melt Ice on Sidewalks ∘\circ∘

Magnesium Chloride Is Often Used to Melt Ice on Sidewalks $\circ$