The complete combustion of salicylic acid releases 21.90 kJ of energy per gram of salicylic acid. In a particular bomb calorimeter (initially at room temperature), the combustion of 0.1182 g of salicylic acid, in the presence of excess oxygen, causes the temperature of the calorimeter to rise by 2.84 °C. When a 0.2086-g sample of an unknown organic substance is similarly burned in the same calorimeter, the temperature rises by 3.50 °C. What is the energy of combustion per unit mass of the unknown substance?
To find the energy of combustion per unit mass of the unknown substance, we can use the energy released and the temperature rise for the known substance to calculate the heat capacity of the calorimeter.
Step 1: Calculate the heat capacity of the calorimeter.
The heat capacity (C) can be calculated using the formula:
C = q / ΔT
where q is the energy released and ΔT is the temperature rise.
For salicylic acid:
q1 = 21.90 kJ/g × 0.1182 g = 2.59 kJ
ΔT1 = 2.84 °C
C1 = q1 / ΔT1 = 2.59 kJ / 2.84 °C = 0.91 kJ/°C
Step 2: Calculate the energy of combustion for the unknown substance.
Using the same calorimeter, the temperature rise for the unknown substance is ΔT2 = 3.50 °C.
To calculate q2, we can rearrange the formula:
q2 = C2 × ΔT2
Substituting the known values into the formula, we have:
0.91 kJ/°C × 3.50 °C = 3.19 kJ
Step 3: Calculate the energy of combustion per unit mass of the unknown substance.
The energy of combustion per unit mass (q/m) can be calculated using the formula:
q/m = q2 / m2
where q2 is the energy released for the unknown substance and m2 is the mass of the unknown substance.
For the unknown substance:
q2 = 3.19 kJ
m2 = 0.2086 g
q/m = 3.19 kJ / 0.2086 g ≈ 15.31 kJ/g
Therefore, the energy of combustion per unit mass of the unknown substance is approximately 15.31 kJ/g.
To find the energy of combustion per unit mass of the unknown substance, we need to use the heat capacity of the bomb calorimeter and the temperature rise caused by the combustion.
The heat capacity of the bomb calorimeter can be calculated using the equation:
Q = mcΔT
Where Q is the heat absorbed by the calorimeter, m is the mass of the substance burned, c is the heat capacity of the calorimeter, and ΔT is the temperature rise.
First, let's calculate the heat absorbed by the calorimeter when salicylic acid is burned:
Q1 = m1 * c * ΔT1
Where m1 = 0.1182 g (mass of salicylic acid burned), ΔT1 = 2.84 °C (temperature rise).
Next, let's calculate the heat absorbed by the calorimeter when the unknown substance is burned:
Q2 = m2 * c * ΔT2
Where m2 = 0.2086 g (mass of the unknown substance burned), ΔT2 = 3.50 °C (temperature rise).
We know that the energy released per gram of salicylic acid is 21.90 kJ. Therefore, the energy released when 0.1182 g of salicylic acid is burned can be calculated as:
Energy1 = 0.1182 g * 21.90 kJ/g = X kJ
Similarly, the energy released when 0.2086 g of the unknown substance is burned can be calculated as:
Energy2 = 0.2086 g * Y kJ/g
Now, we can set up an equation to find the energy of combustion per unit mass of the unknown substance:
Energy2 = Energy1 * (m2 / m1)
Substituting the known values, we have:
0.2086 g * Y kJ/g = X kJ * (0.2086 g / 0.1182 g)
Solving for Y, we get:
Y = (X * (0.2086 g / 0.1182 g)) / 0.2086 g
Simplifying the equation:
Y = X / (0.1182 g / 0.2086 g)
Y = X / (0.1182 / 0.2086)
Now, substitute the given values:
Y = 21.90 kJ / (0.1182 / 0.2086)
Solving for Y, we find:
Y = 21.90 kJ / 0.5666
Y ≈ 38.69 kJ/g
Therefore, the energy of combustion per unit mass of the unknown substance is approximately 38.69 kJ/g.
First determine the heat capacity of the calorimeter.
salicylic acid + O2 ==> CO2 + H2O (not balanced) + 21.90 kJ/gram; therefore
q = 21.90 x 0.1182g = ? kJ
q = heat capacity x delta T
Substitute q and delta T and solve for C (heat capacity) if the calorimeter.
E of combustion = mass sample x heat capacity x delta T. Solve for E combustion and that is 0.2086g sample. Convert to 1 gram of the sample. Watch the units.