Calculate the energy required to heat 795.0mg of ethanol from −2.4°C to 14.6°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 795.0mg of ethanol from −2.4°C to 14.6°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,
- c is the specific heat capacity, and
- ΔT is the change in temperature.
First, convert the mass from milligrams to grams because the specific heat capacity is given in J/g·K.
795.0 mg = 0.795 g
Next, calculate the change in temperature.
ΔT = T_final - T_initial = 14.6°C - (-2.4°C) = 17.0 K
Now, you can substitute the values into the formula:
q = (0.795 g) * (2.44 J/g·K) * (17.0 K) = 32.9 J
So, the energy required to heat 795.0 mg of ethanol from -2.4°C to 14.6°C is approximately 33 J, rounded to the correct number of significant digits.
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