Multiple Choice
Given 307.5 g of hot tea at 73.5 °C, what mass of ice at 0 °C must be added to obtain iced tea at 12.5 °C? The specific heat of the tea is 4.18 J/(g·°C), and ΔHfusion for ice is +6.01 kJ/mol.
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8. Thermochemistry
Endothermic & Exothermic Reactions
Multiple Choice
Given 414.5 g of hot tea at 73.0 °C, what mass of ice at 0 °C must be added to obtain iced tea at 12.0 °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
200.0 g
C
50.0 g
D
100.0 g
Verified step by step guidance1
Identify the heat lost by the hot tea as it cools from 73.0 °C to 12.0 °C. Use the formula for heat transfer: \( q = m \cdot c \cdot \Delta T \), where \( m \) is the mass of the tea, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.
Calculate the change in temperature for the tea: \( \Delta T = T_{final} - T_{initial} = 12.0 \text{ °C} - 73.0 \text{ °C} \).
Substitute the known values into the heat transfer equation to find the heat lost by the tea: \( q_{tea} = 414.5 \text{ g} \times 4.18 \text{ J/(g°C)} \times (12.0 \text{ °C} - 73.0 \text{ °C}) \).
Determine the heat required to melt the ice using the formula: \( q_{ice} = n \cdot \Delta H_{fusion} \), where \( n \) is the number of moles of ice and \( \Delta H_{fusion} \) is the enthalpy of fusion. Convert the mass of ice to moles using the molar mass of water (18.02 g/mol).
Set the heat lost by the tea equal to the heat gained by the ice (since energy is conserved) and solve for the mass of ice: \( q_{tea} = q_{ice} \). Rearrange the equation to find the mass of ice needed.
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