Calculate the energy required to heat 153.0g of ethanol from −4.1°C to 12.8°C. Assume the specific heat capacity of ethanol under these conditions is ·2.44J·g−1K−1 . Be sure your answer has the correct number of significant digits.
Question
Calculate the energy required to heat 153.0g of ethanol from −4.1°C to 12.8°C. Assume the specific heat capacity of ethanol under these conditions is ·2.44J·g−1K−1 . Be sure your answer has the correct number of significant digits.
Solution
To calculate the energy required to heat a substance, you 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 of the substance
- ΔT is the change in temperature
Given:
- m = 153.0 g
- c = 2.44 J/g·K
- Initial temperature (T1) = -4.1°C
- Final temperature (T2) = 12.8°C
First, calculate the change in temperature (ΔT):
ΔT = T2 - T1 ΔT = 12.8°C - (-4.1°C) ΔT = 16.9°C
Then, substitute the values into the formula to find q:
q = mcΔT q = (153.0 g)(2.44 J/g·K)(16.9 K) q = 6385.572 J
So, the energy required to heat 153.0 g of ethanol from -4.1°C to 12.8°C is approximately 6386 J, rounded to four significant digits.
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