Can you check what I did below? On the first problem, I am not sure if I am suppose to add a negative to the first part of the heat loss of water like so -[C(sp)m(w)deltaT(w)]. On the second problem, part(a), I am not sure if I am using the mass from the first problem, 135g, or obtain the mass by multipling 100 mL with the density of water at 45.3*C or 31.8*C, to solve for the heat gained by the solution. Also, I am not sure if I am using the heat of capacity of the calorimeter in the first question to solve part (b). Thanks for the help!
Consider a calorimeter into which 135 g of water at 45.3*C is added. The initial temperature of the calorimeter was 23.8*C and the equilibrium temperature of the water and the calorimeter is 39.8*C. Assuming there is no heat loss to the surroundings, what is the heat capacity of the calorimeter in J/*C?
Heat loss of H20=Heat gain of calorimeter
-[C(sp)m(w)deltaT(w)]=[C(p)deltaT(c)]
-[(4.184 J/g*C)(135g)(39.6*C-45.3*C)]=C(p)(39.6*C-23.8*C)
C(p)=2.0x10^2 J/*C
In another experiment, 11.6 g of a salt was dissolved in 100.0 mL of water contained in the above calorimeter, all at an initial temperature of 24.5*C. After dissolution was complete, the temperature was 31.8*C. The specific heat of the solution is 3.63 J/g*C and the molar mass of the salt is 153.5 g/mol. Assume there is no heat loss to the surroundings.
a)Calculate the heat gained by the solution
Q(solution)=CM(solution)deltaT(solution)
=(3.63 J/g*C)(11.6g +135g)(31.8*C-24.5*C)
=3.88x10^3 J
b)Calculate the heat gained by the calorimeter
Q(c)=C(p)deltaT(c)
=(2.0x10^2 J/*C)(39.6*C-23.8*C)
=3.2x10^3 J
c)Calculate the total heat gained by the system
(3.9x10^3 J) + (3.2x10^3 J) = 7.1 x 10^3 J
d)Calculate the heat of solution (deltaH) of the salt in J/mol
(7.1x10^3 J)/[(11.6)(1 mol/153.5g)]
=(7.1x10^3 J)/ .0756 mol = 9.4 x 10^4 J/mol
6 answers
The sign depends upon so many things; e.g., if we use Tf-Ti for delta T or just delta T and if we use heat lost = heat gained OR if we use heat lost + heat gained = 0. Frankly, I can get so confused with all of that that I prefer to use
mass water x specific heat water x (Tf-Ti) + Cp calorimeter x (Tf-Ti) = 0. THE SIGNS THEN TAKE CARE OF THEMSELVES.
I would point out two or three things.
1. The problem quotes 39.8o C but you used 39.6 for T in your calculations. That makes a small difference.
I'll do the others as a separate response.
mass x specific heat x (Tf-Ti).
The 135 g H2O was in the other problem, not this one so forget it. The number you want here is, technically, 100.0 mL H2O x density water at 31.8 BUT since density is not given in the problem, my best guess is that the authors intended you to use 100.0 mL = 100.0 grams. So Q = 100.0 x 3.63 x (31.8-24.5) = ??
b.
Q calorimeter = Cp x (Tf-Ti). Again, you are using numbers from the first problem. Using from this problem Tf = 31.8 and Ti = 24.5.
c.
The total heat gained by the system must be the heat absorbed by the solution + the heat absorbed by the calorimeter or answer from a + answer from b.
d.
heat solution in j/mol = total heat/mols salt.
mols salt = 11.6/153.5
For the 100 mL, I assume my teacher wants me to look up the denisty in the appendix of our lab notebook. Am I suppose to look up the density of water at 24.5*C, which is 0.997914g/ml?
Wouldn't the heat capacity of the calorimeter be different for part c) if I am not using 135 g water?
The one thing that troubles me the most is that the second problem refers to the water contained in the above calorimeter.
Thanks for the help DrBob222!
1) Consider a calorimeter into which 135 g of water at 45.3*C is added. The initial temperature of the calorimeter was 23.8*C and the equilibrium temperature of the water and the calorimeter is 39.6*C. Assuming there is no heat loss to the surroundings, what is the heat capacity of the calorimeter in J/*C?
Heat loss of H20=Heat gain of calorimeter
-[C(sp)m(w)deltaT(w)]=[C(p)deltaT(c)]
-[(4.184 J/g*C)(135g)(39.6*C-45.3*C)]=C(p)(39.6*C-23.8*C)
C(p)=2.0x10^2 J/*C
2) In another experiment, 11.6 g of a salt was dissolved in 100.0 mL of water contained in the above calorimeter, all at an initial temperature of 24.5*C. After dissolution was complete, the temperature was 31.8*C. The specific heat of the solution is 3.63 J/g*C and the molar mass of the salt is 153.5 g/mol. Assume there is no heat loss to the surroundings.
a)Calculate the heat gained by the solution
Q(solution)=CM(solution)deltaT(solution)
(3.63 J/g*C)(11.6g + (100ml)(0.997914g/ml))(31.8*C-24.5*C)=3.0x10^3 J
b)Calculate the heat gained by the calorimeter
Q(c)=C(p)deltaT(c)
=(2.0x10^2 J/*C)(31.8*C-24.5*C)
=4.5x10^3 J
c)Calculate the total heat gained by the system
(3.0x10^3 J) + (1.5x10^3 J) = 4.5 x 10^3 J
d)Calculate the heat of solution (deltaH) of the salt in J/mol
(4.5x10^3 J)/[(11.6)(1 mol/153.5g)]
=(4.5x10^3 J)/ .0756 mol = -6.0 x 10^4 J/mol
For the 100 mL, I assume my teacher wants me to look up the density in the appendix of our lab notebook. Am I supposed to look up the density of water at 24.5*C, which is 0.997914g/ml?
If you are to go the density route, I think you want to look up the density at the FINAL temperature. The final T is the one at which equilibrium is reached so that will determine the final mass of water. Most problems of this type I have seen say to assume the solution has a density of 1.0; however, with 11.6 g of a salt and only 100.0 mL water, I can see that the density probably will NOT be 1.00 if that is all the water used. But see my next comment; I think you have closer to 235 g water. Even then, however, the water might be significantly different from a density of 1.00, expecially for accurate calculations.
Wouldn't the heat capacity of the calorimeter be different for part c) if I am not using 135 g water?
Heat capacity is heat capacity. The way I have interpreted the problem is that the 100.0 mL plus the salt is added to the existing 135 g water + the container of the calorimeter. Therefore, the heat capacity of the 135 g water + the container is taken into account by Cp*delta T (for the experiment, not delta T for the heat capacity determination) and you don't add in the extra water for the 100.0 mL + salt.
The one thing that troubles me the most is that the second problem refers to the water contained in the above calorimeter.
That's why I interpreted as I explained above. USUALLY, the heat capacity of a calorimeter is determined in this type experiment with a certain amount of water and that amount of water is used each time.