The formation of condensation on a glass of ice water causes the ice
to melt faster than it would otherwise. If 8.00 g of condensation forms 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.
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To determine how many grams of ice will melt as a result of the condensation, we need to calculate the amount of heat transferred from the condensation to the ice.
First, we need to determine the amount of heat transferred during the phase change from vapor to liquid for the condensation. The heat transferred during a phase change is given by the equation:
Q = m × ΔH
Where:
Q is the heat transferred
m is the mass of the substance (in this case, condensation)
ΔH is the heat of vaporization for the substance (in this case, water)
The heat of vaporization for water is 40.7 kJ/mol, or 40.7 J/g.
To calculate the heat transferred, we need to convert the mass of condensation from grams to moles, as the heat of vaporization is given in J/mol. The molar mass of water is 18.02 g/mol.
Number of moles of condensation = mass of condensation / molar mass of water
Number of moles of condensation = 8.00 g / 18.02 g/mol
Next, we can calculate the amount of heat transferred:
Q = m × ΔH
Q = (number of moles of condensation) × ΔH
To convert the heat transferred to grams of ice melted, we need to know the heat of fusion for water, which is 334 J/g.
The number of grams of ice melted can be calculated using the equation:
Grams of ice melted = Q / ΔH
Substituting the values:
Grams of ice melted = [(number of moles of condensation) × ΔH] / ΔH
The ΔH cancels out:
Grams of ice melted = number of moles of condensation
Plugging in the calculated value for the number of moles of condensation, we can find the answer:
Grams of ice melted = 8.00 g / 18.02 g/mol
After performing the calculation, the grams of ice melted as a result of the condensation will be obtained.