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Multiple Choice
Given 382.0 g of hot tea at 82.0 °C, what mass of ice at 0 °C must be added to obtain iced tea at 15.0 °C? The specific heat of the tea is 4.18 J/(g·°C), and ΔHfusion for ice is +6.01 kJ/mol.
A
150.0 g
B
50.0 g
C
100.0 g
D
200.0 g
Verified step by step guidance
1
Step 1: Identify the heat lost by the tea as it cools from 82.0 °C to 15.0 °C. Use the formula for heat transfer: , where is the mass of the tea, is the specific heat capacity, and is the change in temperature.
Step 2: Calculate the heat required to melt the ice using the formula: , where is the number of moles of ice and is the enthalpy of fusion.
Step 3: Convert the mass of ice to moles using the molar mass of water (18.02 g/mol). This will allow you to use the enthalpy of fusion in the calculation.
Step 4: Set up an equation where the heat lost by the tea equals the heat gained by the ice. This is based on the principle of conservation of energy: .
Step 5: Solve the equation for the mass of ice required. This involves rearranging the equation and substituting the known values to find the mass of ice that will absorb the heat lost by the tea.