Calculate the amount of heat required to raise the temperature of 851.2 mL of a solution from 22.9 °C to 35.2 °C if the solution has a density of 1.04 g mL–1 and a heat capacity of 4.08 J K–1 g–1.
Question
Calculate the amount of heat required to raise the temperature of 851.2 mL of a solution from 22.9 °C to 35.2 °C if the solution has a density of 1.04 g mL–1 and a heat capacity of 4.08 J K–1 g–1.
Solution
Sure, here are the steps to calculate the amount of heat required:
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First, calculate the mass of the solution. The density of the solution is given as 1.04 g/mL, so the mass (m) can be calculated by multiplying the volume (V) by the density (ρ).
m = V * ρ = 851.2 mL * 1.04 g/mL = 884.448 g
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Next, calculate the change in temperature (ΔT). This is the final temperature (Tf) minus the initial temperature (Ti).
ΔT = Tf - Ti = 35.2 °C - 22.9 °C = 12.3 °C
Note: The Celsius scale is the same as the Kelvin scale in terms of intervals, so a change of 1 degree Celsius is equivalent to a change of 1 Kelvin. Therefore, we can use the Celsius change directly in the formula.
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Finally, calculate the heat (q) using the formula q = m * c * ΔT, where c is the heat capacity.
q = m * c * ΔT = 884.448 g * 4.08 J/(g*K) * 12.3 K = 44360.6 J
So, the amount of heat required to raise the temperature of the solution from 22.9 °C to 35.2 °C is approximately 44360.6 Joules.
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