Multiple Choice
How much energy is needed to raise the temperature of 5.0 grams of lead from 25°C to 35°C? [specific heat (c) = 0.129 J/(g°C)]
1. Intro to General Chemistry
Temperature
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What volume of water (in mL), initially at 75.6 °C, needs to be mixed with 229 mL of water, initially at 20.7 °C, so that the final temperature of the water is 41.8 °C? Assume that the density of water remains constant over the above temperature range.
A
100 mL
B
150 mL
C
250 mL
D
200 mL
Verified step by step guidance1
Identify the principle of conservation of energy, which states that the heat lost by the hot water will be equal to the heat gained by the cold water.
Use the formula for heat transfer: \( q = m \cdot c \cdot \Delta T \), where \( q \) is the heat energy, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.
Assume the density of water is 1 g/mL, so the mass of water is equal to its volume in mL. Therefore, the mass of the cold water is 229 g and the mass of the hot water is \( x \) g, where \( x \) is the volume of hot water in mL.
Set up the equation for heat transfer: \( m_{hot} \cdot c \cdot (T_{final} - T_{hot}) = m_{cold} \cdot c \cdot (T_{final} - T_{cold}) \). Substitute the known values: \( x \cdot 4.18 \cdot (41.8 - 75.6) = 229 \cdot 4.18 \cdot (41.8 - 20.7) \).
Solve the equation for \( x \) to find the volume of hot water needed. Simplify and calculate \( x \) to determine the volume in mL.
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