A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 3.00kg of water at 22.0°C. During the reaction 114.kJ of heat flows out of the bath and into the flask.Calculate the new temperature of the water bath. You can assume the specific heat capacity of water under these conditions is 4.18·J·g−1K−1. Be sure your answer has the correct number of significant digits.°C
Question
A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 3.00kg of water at 22.0°C. During the reaction 114.kJ of heat flows out of the bath and into the flask.Calculate the new temperature of the water bath. You can assume the specific heat capacity of water under these conditions is 4.18·J·g−1K−1. Be sure your answer has the correct number of significant digits.°C
Solution
To solve this problem, we need to use the formula for heat transfer:
q = mcΔT
where: q = heat energy (in joules) m = mass (in grams) c = specific heat capacity (in joules per gram per degree Celsius) ΔT = change in temperature (in degrees Celsius)
First, we need to convert the mass of the water from kg to g, because the specific heat capacity is given in J/g·K.
3.00 kg = 3000 g
Next, we need to convert the heat energy from kJ to J, because the specific heat capacity is given in J/g·K.
114 kJ = 114,000 J
We know that the heat energy is flowing out of the water, so it is losing energy. Therefore, the heat energy is negative:
q = -114,000 J
Now we can plug the known values into the formula and solve for ΔT:
-114,000 J = (3000 g)(4.18 J/g·K)(ΔT)
Solving for ΔT gives:
ΔT = -114,000 J / [(3000 g)(4.18 J/g·K)] = -9.1°C
The change in temperature is negative because the water is cooling down. To find the final temperature of the water, we subtract the change in temperature from the initial temperature:
Final temperature = initial temperature - ΔT = 22.0°C - (-9.1°C) = 31.1°C
So, the final temperature of the water bath is 31.1°C.
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