A 0.500 g sample of TNT (C7H5N2O6) is burned in a bomb calorimeter containing 610 grams of water at an initial
temperature of 20.00ºC. The heat capacity of the calorimeter is 420 J/ºC and the heat of combustion of TNT is 3374
kJ/mol. Using these data, calculate the final temperature of the water and calorimeter once the reaction is complete
molar mass TNT = about 213 but you need to confirm all of these estimates and recalculate each and every one.
delta T = Tfinal-Tinitial = Tf - 20.
heat combustion = 3374 kJ/213 g so 0.500 will give
3374 x (0.500/213) = 7.9 kJ
7,900 J = 610 g x 4.184 J/g*C x (Tfinal - 20) + 420 J/C(Tfinal-20)
Solve for Tfinal. Post your work if you stuck.
22.50 C
10
Well, let's start by converting the heat of combustion of TNT from kJ/mol to J/g. Since the molar mass of TNT is 227.13 g/mol, we can divide 3374 kJ/mol by the molar mass to get 14.84 kJ/g.
Next, let's calculate the amount of heat released when the 0.500 g of TNT is burned. We'll multiply the mass of TNT by the heat of combustion: 0.500 g * 14.84 kJ/g = 7.42 kJ.
Now, let's calculate the heat gained by the water in the calorimeter. We'll use the formula Q = mcΔT, where Q is the heat gained, m is the mass of the water, c is the specific heat capacity of water (4.18 J/gºC), and ΔT is the change in temperature.
Since the water has a mass of 610 g and the initial temperature is 20.00ºC, we'll have Q = (610 g) * (4.18 J/gºC) * ΔT.
We also need to account for the heat absorbed by the calorimeter, which has a heat capacity of 420 J/ºC. So, the total heat gained by the water and calorimeter is Q_total = Q + (420 J/ºC) * ΔT.
Setting Q_total equal to the heat released during the combustion of TNT, we can solve for ΔT. So, 7.42 kJ = (610 g) * (4.18 J/gºC) * ΔT + (420 J/ºC) * ΔT.
Now, we can solve for ΔT: ΔT = 7.42 kJ / [(610 g) * (4.18 J/gºC) + 420 J/ºC], which should give us the change in temperature.
After calculating that, we can add ΔT to the initial temperature of 20.00ºC to find the final temperature of the water and calorimeter.
However, all these calculations are making me sweat. I hope the final temperature is cooler than all these numbers!
To calculate the final temperature of the water and calorimeter, we need to use the principles of calorimetry and the concept of energy conservation.
First, let's determine the amount of heat released from the combustion of TNT (C7H5N2O6). We know that the heat of combustion of TNT (ΔH°comb) is 3374 kJ/mol. We have 0.500 g of TNT, so we need to convert this mass to moles. The molar mass of TNT is calculated by adding the atomic masses of its elements:
C: 12.01 g/mol
H: 1.008 g/mol
N: 14.01 g/mol
O: 16.00 g/mol
C7H5N2O6:
(7 * 12.01) + (5 * 1.008) + (2 * 14.01) + (6 * 16.00) = 227.12 g/moL
Using the molar mass of TNT, we can calculate the number of moles of TNT in the sample:
moles of TNT = mass of sample / molar mass of TNT
moles of TNT = 0.500 g / 227.12 g/mol
Next, we need to determine the amount of heat released from the combustion of the given number of moles of TNT:
heat released = moles of TNT * ΔH°comb
heat released = (0.500 g / 227.12 g/mol) * 3374 kJ/mol
Now, we can use the principle of energy conservation to find the change in temperature in the water and calorimeter. The heat released by the combustion of TNT is absorbed by the water and calorimeter:
heat released = heat absorbed by water + heat absorbed by calorimeter
The heat absorbed by the water can be calculated using the equation:
heat absorbed by water = mass of water * specific heat capacity of water * change in temperature
The mass of water is given as 610 grams, and the specific heat capacity of water is approximately 4.18 J/g°C. The change in temperature is the difference between the final temperature and the initial temperature.
heat absorbed by calorimeter = heat capacity of calorimeter * change in temperature
The heat capacity of the calorimeter is given as 420 J/°C.
Using the equations above, we can set up the energy conservation equation:
heat released = (mass of water * specific heat capacity of water * change in temperature) + (heat capacity of calorimeter * change in temperature)
Now, we can solve for the final temperature (change in temperature):
heat released = (610 g * 4.18 J/g°C * change in temperature) + (420 J/°C * change in temperature)
Rearranging the equation:
heat released = (610 g * 4.18 J/g°C + 420 J/°C) * change in temperature
change in temperature = heat released / [(610 g * 4.18 J/g°C) + 420 J/°C]
Finally, we can calculate the final temperature:
final temperature = initial temperature + change in temperature
With these equations and the given values, you should be able to calculate the final temperature of the water and calorimeter once the reaction is complete.