The combustion of 0.1583 g benzoic acid increases the temperature of a bomb calorimeter by 2.93°C. Calculate the heat capacity of this calorimeter. (The energy released by combustion of benzoic acid is 26.42 kJ/g.)
A 0.1710 g sample of vanillin (C8H8O3) is then burned in the same calorimeter, and the temperature increases by 3.25°C. What is the energy of combustion per gram of vanillin?
What is the energy of combustuin per mole of vanillin?
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НыгН
To calculate the heat capacity of the calorimeter, we need to use the formula:
Q = m * C * ΔT
Where:
Q = heat absorbed or released by the system (calorimeter)
m = mass of the substance being burned
C = heat capacity of the calorimeter
ΔT = change in temperature
For the first part of the question, we can use the given information to calculate the heat capacity of the calorimeter.
Given:
Mass of benzoic acid (m) = 0.1583 g
Change in temperature (ΔT) = 2.93°C
Energy released by combustion of benzoic acid = 26.42 kJ/g
First, convert the mass of benzoic acid to grams:
m = 0.1583 g
Next, calculate the heat generated by the combustion of benzoic acid:
Q = m * ΔT * C
We know the Q value from the energy released by combustion of benzoic acid, which is 26.42 kJ/g. Convert it to joules:
Q = (26.42 kJ/g) * (0.1583 g) * (1000 J/kJ) = 4175.8 J
Now, substitute the values into the formula and solve for C:
4175.8 J = (0.1583 g) * C * (2.93°C)
C = 4175.8 J / [(0.1583 g) * (2.93°C)] ≈ 9294 J/g°C
So, the heat capacity of the calorimeter is approximately 9294 J/g°C.
For the second part of the question, we can use the same formula to calculate the energy of combustion per gram of vanillin.
Given:
Mass of vanillin (m) = 0.1710 g
Change in temperature (ΔT) = 3.25°C
Again, substitute the values into the formula and solve for Q:
Q = (0.1710 g) * C * (3.25°C)
Since we already know the heat capacity of the calorimeter (C), we can calculate Q directly:
Q = (0.1710 g) * (9294 J/g°C) * (3.25°C)
Q ≈ 5336.2 J
So, the energy of combustion per gram of vanillin is approximately 5336.2 J.
Now, to calculate the energy of combustion per mole of vanillin, we need to know the molar mass of vanillin (C8H8O3). The molar mass of carbon (C) is approximately 12.01 g/mol, hydrogen (H) is approximately 1.01 g/mol, and oxygen (O) is approximately 16.00 g/mol.
Molar mass of vanillin (C8H8O3) = (8 * 12.01 g/mol) + (8 * 1.01 g/mol) + (3 * 16.00 g/mol)
Molar mass of vanillin (C8H8O3) ≈ 152.15 g/mol
To calculate the energy of combustion per mole of vanillin, divide the energy of combustion per gram of vanillin by its molar mass:
Energy of combustion per mole of vanillin = (5336.2 J) / (0.1710 g) / (152.15 g/mol)
Energy of combustion per mole of vanillin ≈ 19.4 kJ/mol
So, the energy of combustion per mole of vanillin is approximately 19.4 kJ/mol.