The formation of condensation on a glass of ice water causes the ice to melt faster than it would otherwise. If 7.40 g of condensation forms on a glass containing water and 210 g of ice, how many grams will melt as a result? Assume no other heat transfer occurs. Use the heat of vaporization of water at 37°, as an approximation, in this problem.
At 37.0ºC the heat of vaporization Lv for water is 2430 kJ/kg or 580 kcal/kg.
Heat of Fusion and vaporization at 0℃ for water(ice) L(f)= 334 kJ/kg.
m(cond) •L(v)=ML(f)
M= m(cond) •L(v)/ L(f)=
=7.4•10⁻³•2430000/334000 =5.38•10⁻² kg = =53.8 g
To solve this problem, we need to calculate the amount of heat transferred during the phase change from liquid to gas for the 7.40 g of condensation. We can then use this information to determine the amount of ice that will melt as a result.
1. Calculate the heat transferred during the phase change:
The heat of vaporization of water is the amount of heat required to convert 1 gram of water from liquid to gas at a given temperature. In this case, we'll use the heat of vaporization at 37°C.
The heat transfer formula is:
q = m * ΔHvap
where q is the heat transferred, m is the mass, and ΔHvap is the heat of vaporization.
Let's calculate the heat transferred for the 7.40 g of condensation:
q = 7.40 g * ΔHvap
2. Determine the amount of ice that will melt:
The heat transferred during the phase change for the condensation will cause an equal amount of ice to melt.
We can calculate the mass of ice that will melt using the heat transfer formula:
q = m * ΔHfusion
where q is the heat transferred, m is the mass, and ΔHfusion is the heat of fusion.
Let's calculate the mass of ice that will melt:
q = m * ΔHfusion
Now, we have all the information needed to solve the problem. Let's proceed with the calculations.
Note: Since the values for ΔHvap and ΔHfusion are not provided, we will assume standard values, which are 40.7 kJ/mol and 6.01 kJ/mol, respectively. These values will allow us to calculate the answer in grams.
1. Calculate the heat transferred during phase change:
q = 7.40 g * (40.7 kJ/mol / 18.02 g/mol)
Now, let's convert the heat transferred to grams of ice melted.
2. Determine the amount of ice that will melt:
q = m * ΔHfusion
q = m * (6.01 kJ/mol / 18.02 g/mol)
Now, let's substitute the values we calculated for q into the equation and solve for m:
7.40 g * (40.7 kJ/mol / 18.02 g/mol) = m * (6.01 kJ/mol / 18.02 g/mol)
Calculate the mass of ice melted (m):
m = (7.40 g * (40.7 kJ/mol / 18.02 g/mol)) / (6.01 kJ/mol / 18.02 g/mol)
m = 52.1 g
Therefore, as a result of the condensation, approximately 52.1 grams of ice will melt.
To determine the grams of ice that will melt due to the formation of condensation, we need to calculate the amount of heat transferred from the water to the ice.
The heat released by the condensation of 7.40 g of water vapor can be calculated using the formula:
Q = m * H
Where:
Q = heat released
m = mass of condensation
H = heat of condensation
Using the heat of vaporization of water at 37°C as an approximation, the value of H is 2260 J/g.
Substituting the values into the formula, we have:
Q = 7.40 g * 2260 J/g
Q = 16684 J
The heat released by the condensation is equal to the heat gained by the ice, causing it to melt. The heat required to melt ice can be calculated using the formula:
Q = m * Hm
Where:
Q = heat required
m = mass of ice
Hm = heat of fusion
The heat of fusion of ice is 333.55 J/g.
Substituting the values into the formula, we have:
16684 J = m * 333.55 J/g
Solving for m:
m = 16684 J / 333.55 J/g
m ≈ 49.997 g
Approximately 50 g of ice will melt as a result of the condensation.