Question

Condensation on a glass of ice water causes the ice to melt faster than it would otherwise. If 8.00 g of vapor condense on a glass containing both water and 200 g of ice, how many grams of the ice will melt as a result? Assume no other heat transfer occurs. Use Lv for water at 37°C as a better approximation than Lv for water at 100°C.)

a) 3.54 g
b) 7.08 g
c) 14.17 g
d) 28.34 g

Answer 1

To calculate how many grams of ice will melt as a result of 8.00 g of water vapor condensing on a glass with ice, the latent heat of vaporization and fusion must be used. Approximately 57.49 grams of the ice will melt as a result of the condensation. So, none of the given options are correct.

Step-by-step explanation:

To find the grams of ice that will melt, we need to calculate the amount of heat transferred when 8.00 g of vapor condenses.

We can use the equation Q = m * Lv, where Q is the heat transferred, m is the mass, and Lv is the heat of vaporization.

Assuming Lv for water at 37°C is 2400 J/g, we can calculate the heat transferred Q = (8.00 g) * (2400 J/g).

This gives us Q = 19200 J.

Next, we need to calculate the amount of heat required to melt the ice. We can use the equation Q = m * Lf, where Lf is the heat of fusion.

Assuming Lf for ice is 334 J/g, we can calculate the heat required to melt the ice Q = (200 g) * (334 J/g).

This gives us Q = 66800 J.

Since the heat transferred from condensation is less than the heat required to melt the ice, only a portion of the ice will melt.

Let's calculate the mass of the ice that will melt. Q = m * Lf, so m = Q / Lf.

Using the values we calculated, m = (19200 J) / (334 J/g).

This gives us m = 57.49 g.

Therefore, approximately 57.49 grams of the ice will melt as a result of the condensation.

None of the given options are correct.