Multiple Choice
Determine whether the process of dry ice evaporating is endothermic or exothermic and indicate the sign of ΔH.
8. Thermochemistry
Endothermic & Exothermic Reactions
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Given 313.5 g of hot tea at 72.5 °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.
A
135.0 g
B
45.0 g
C
105.0 g
D
75.0 g
Verified step by step guidance1
Identify the heat lost by the hot tea as it cools from 72.5 °C to 12.5 °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: \( \Delta T = 72.5 \text{ °C} - 12.5 \text{ °C} \).
Calculate the heat lost by the tea using the specific heat capacity: \( q_{\text{tea}} = 313.5 \text{ g} \times 4.18 \text{ J/(g·°C)} \times \Delta T \).
Determine the heat required to melt the ice using the formula: \( q = n \cdot \Delta H_{\text{fusion}} \), where \( n \) is the number of moles of ice and \( \Delta H_{\text{fusion}} \) 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 to find the mass of ice needed: \( q_{\text{tea}} = q_{\text{ice}} \). Solve for the mass of ice.
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