An electrical heater is used to add 19.50 kJ of heat to a constant-volume calorimeter. The temperature of the calorimeter increases by 4.50°C. When 1.75 g of butanol (C4H9OH) is burned in the same calorimeter, the temperature increases by 14.58°C. Calculate the molar heat of combustion for butanol (enter in kJ).
Ccal = 19,500 Joules/4.5 C = 4333.33 J/C.
For 1.75 butanol, moles
1.75 x (1 mol butanol/74.123) = ??
heat generated = 14.58 C x 4,333.33 J/C = 63,179.95 Joules and that divided by moles should give you the heat of combustion per mole. I get something like 2,676 kJ/mol.
To calculate the molar heat of combustion for butanol (C4H9OH), we need to use the heat gained by the calorimeter when the butanol is burned.
First, let's calculate the heat gained when the electrical heater is used. We know that the heat gained is 19.50 kJ and the temperature increase is 4.50°C. Since the calorimeter is constant volume, we can use the equation:
q = CΔT
Where q is the heat gained, C is the heat capacity of the calorimeter, and ΔT is the temperature increase.
For the electrical heater:
q1 = CΔT1
19.50 kJ = CΔT1
Next, let's calculate the heat gained when the butanol is burned. We know that the heat gained is 14.58°C and the mass of butanol burned is 1.75 g. To calculate the heat gained during combustion, we can use the equation:
q2 = mCΔT2
Where q2 is the heat gained during combustion, m is the mass of butanol burned, C is the specific heat capacity of butanol, and ΔT2 is the temperature increase.
For the butanol combustion:
q2 = mCΔT2
14.58°C = (1.75 g)CΔT2
Now, let's substitute the values into the equations and solve for C, the specific heat capacity of butanol:
19.50 kJ = CΔT1
14.58°C = (1.75 g)CΔT2
Rearranging the first equation to solve for C:
C = 19.50 kJ / ΔT1
Substituting the value of C from the first equation into the second equation:
14.58°C = (1.75 g) (19.50 kJ / ΔT1) ΔT2
Simplifying the equation:
14.58°C = 34.125 kJ / ΔT1 ΔT2
Now, we need to solve for ΔT1 ΔT2:
ΔT1 ΔT2 = 34.125 kJ / 14.58°C
Now, let's calculate the value of ΔT1 ΔT2:
ΔT1 ΔT2 = 2.338 kJ/°C
Finally, to calculate the molar heat of combustion, we need to know the number of moles of butanol burned. We can calculate this using the molar mass of butanol:
Molar mass of butanol (C4H9OH) = (4 * Atomic mass of carbon) + (9 * Atomic mass of hydrogen) + Atomic mass of oxygen + Atomic mass of hydrogen
= (4 * 12.01 g/mol) + (9 * 1.01 g/mol) + 16.00 g/mol + 1.01 g/mol
= 74.12 g/mol
Number of moles of butanol burned = Mass of butanol burned / Molar mass of butanol
= 1.75 g / 74.12 g/mol
= 0.02363 mol
To calculate the molar heat of combustion, we divide the heat gained during combustion by the number of moles of butanol burned:
Molar heat of combustion = ΔT1 ΔT2 / Number of moles of butanol burned
= 2.338 kJ/°C / 0.02363 mol
= 98.97 kJ/mol
Therefore, the molar heat of combustion for butanol is 98.97 kJ/mol.