Calculate the amount of heat required to raise the temperature of 825.8 mL of a solution from 22.4 °C to 40.4 °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 1Answer63.1 kJ60.6 kJ58.3 kJ3.79 kJ
Question
Calculate the amount of heat required to raise the temperature of 825.8 mL of a solution from 22.4 °C to 40.4 °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 1Answer63.1 kJ60.6 kJ58.3 kJ3.79 kJ
Solution
To calculate the amount of heat required, we can use the formula:
q = mcΔT
where:
- q is the heat energy
- m is the mass of the substance
- c is the specific heat capacity
- ΔT is the change in temperature
First, we need to calculate the mass of the solution. We can do this by multiplying the volume of the solution by its density:
m = 825.8 mL * 1.04 g/mL = 858.832 g
Next, we calculate the change in temperature:
ΔT = 40.4°C - 22.4°C = 18°C = 18 K (since the change in temperature is the same in Celsius and Kelvin)
Now we can substitute these values into the formula:
q = 858.832 g * 4.08 J/(g*K) * 18 K = 63168.6 J
Since the answer choices are given in kJ, we need to convert J to kJ by dividing by 1000:
q = 63168.6 J / 1000 = 63.1686 kJ
So, the closest answer is 63.1 kJ.
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