Textbook Question
(a) What amount of heat (in joules) is required to raise the temperature of 1 g of water by 1 kelvin? (b) What amount of heat (in joules) is required to raise the temperature of 1 mole of water by 1 kelvin?
8. Thermochemistry
Heat Capacity
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A 28.5 g piece of gold is heated and then allowed to cool. What is the change in temperature (°C) if the gold releases 0.231 kJ of heat as it cools? The molar heat capacity of gold is 25.4 J/mol∙°C. (Atomic mass of gold = 197 g/mol)
A
5.2°C
B
7.1°C
C
3.5°C
D
9.0°C
Verified step by step guidance1
First, convert the mass of gold from grams to moles using the atomic mass of gold. Use the formula: \( \text{moles of gold} = \frac{\text{mass of gold (g)}}{\text{atomic mass of gold (g/mol)}} \).
Next, calculate the heat released in joules. Since the heat is given in kilojoules, convert it to joules by multiplying by 1000: \( \text{heat (J)} = \text{heat (kJ)} \times 1000 \).
Use the formula for heat transfer: \( q = m \cdot C \cdot \Delta T \), where \( q \) is the heat released, \( m \) is the moles of gold, \( C \) is the molar heat capacity, and \( \Delta T \) is the change in temperature.
Rearrange the formula to solve for the change in temperature: \( \Delta T = \frac{q}{m \cdot C} \).
Substitute the values for \( q \), \( m \), and \( C \) into the equation to find \( \Delta T \).
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