The fluorocarbon compound C2Cl3F3 has a normal boiling point of 47.6 ∘C. The specific heats of C2Cl3F3(l) and C2Cl3F3(g) are 0.91 J/g⋅K and 0.67 J/g⋅K, respectively. The heat of vaporization for the compound is 27.49 kJ/mol. Calculate the heat required to convert 47.5g of C2Cl3F3 from a liquid at 10.60∘C to a gas at 81.80∘C.
a. First, I used Q=mCdeltaH for liquid C2Cl3F3
47.5g x .91 J/g-K x (47.6-10.6) = 1599.3
b. Than, I used the same equation to find the heat for it to vaporize.
(47.5g/187.5 g/mol) x 27.49 kJ/mol x 1000J = 6964.1
c. Last, I had to find what the energy would be to warm it to 81 from its boiling point.
47.5g x .67J/g-k x (81.8-47.6) = 1088.4
Adding a+b+c to get the total energy, I got 9651.82, or with 2 sigfigs, 9700 kJ.
I am not sure what I am doing wrong, but 9700 is not the right answer, would love any help I can get!
10 kj
Thanks for showing your work. Your work looks ok and the substitutions look ok.
I think the trouble may be the number of s.f.. If I round a to 1.6E3 (2 s.f.) and add to b rounded to 3 s.f. of 6.96E3 and add to c rounded to 2 s.f. of 1.1E3, I get 9.66E3 which rounded gives 9.7E3 to 2 s.f. Try changing your answer to 9.7E3.
The only other thing I noted was I obtained 187.325 for the molar mass of the compound I didn't go through and see if that will make a different of one digit in the answer or not. My quick guess is that it will not. It is enough to make that b phase 9.97E3 instead of 6.96 but that isn't enough to change the final number.
Your calculations are precise; however, your final calculation is 9700 J. You are answering as kJ. You must convert to 9.70 kJ.
Well, it looks like you've made a small mistake in your calculations. Let's go over the calculations again.
a. The heat required to raise the temperature of the liquid C2Cl3F3:
Q = mCdeltaT
Q = 47.5g * 0.91 J/g⋅K * (81.8 - 10.6) °C
Q = 47.5g * 0.91 J/g⋅K * 71.2 °C
Q = 3053.12 J
b. The heat required for the compound to vaporize:
Q = nΔHvap
First, we need to calculate the number of moles of C2Cl3F3:
n = mass / molar mass
n = 47.5g / 187.5 g/mol
n = 0.25333 mol
Now we can calculate the heat required:
Q = 0.25333 mol * 27.49 kJ/mol * 1000 J/kJ
Q = 6909.42 J
c. The heat required to raise the temperature of the gas C2Cl3F3:
Q = mCdeltaT
Q = 47.5g * 0.67 J/g⋅K * (81.8 - 47.6) °C
Q = 47.5g * 0.67 J/g⋅K * 34.2 °C
Q = 1104.15 J
Now, let's add up the three heat values:
3053.12 J + 6909.42 J + 1104.15 J = 11066.69 J
So, the correct answer is 11066.69 J, or rounded to two significant figures, 11000 J.
Keep up the good work!
To calculate the heat required to convert 47.5g of C2Cl3F3 from a liquid at 10.60∘C to a gas at 81.80∘C, you need to consider three steps: heating the liquid to its boiling point, vaporizing the liquid, and then heating the resulting gas to the final temperature.
a. Heating the liquid:
You correctly calculated the heat required to raise the temperature of the liquid C2Cl3F3 from 10.60∘C to its boiling point (47.6∘C) using the formula Q = mCΔT.
Q1 = 47.5g x 0.91 J/g⋅K x (47.6 - 10.6) = 1599.3 J
b. Vaporization:
To calculate the heat required for vaporization, you need to use the formula Q = nΔHvap, where n is the number of moles of C2Cl3F3 and ΔHvap is the molar heat of vaporization.
First, calculate the number of moles using the molar mass of C2Cl3F3, which is 187.5 g/mol.
n = 47.5g / 187.5 g/mol = 0.2533 mol
Now, calculate the heat of vaporization:
Q2 = 0.2533 mol x 27.49 kJ/mol x 1000 J = 6845.6 J
c. Heating the gas:
Finally, calculate the heat required to raise the temperature of the gas from its boiling point to 81.80∘C using the same formula Q = mCΔT.
Q3 = 47.5g x 0.67 J/g⋅K x (81.8 - 47.6) = 1109.26 J
Now, add the heats calculated in each step to find the total heat required:
Total heat = Q1 + Q2 + Q3 = 1599.3 J + 6845.6 J + 1109.26 J = 9554.16 J
Rounded to two significant figures, the answer is 9600 J (not kJ, as stated in your original question).
Therefore, the correct answer should be 9600 J, not 9700 kJ.