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?
please I want to see the final answer.
21.90 kJ/g x 0.1182 g = ?q = energy obtained by combusting salicylic acid.
Then calculate the heat capacity of the calorimeter. That is
q from above = C/degree c x 2.84 and solve for C, the heat capacity of the calorimeter.
q = heat capacity x delta T
q = Cfrom above x 3.50
Solve for q and that is q/0.2086g and that gives you q/gram of the unknown.
To find the energy of combustion per unit mass of the unknown substance, we can use the heat transfer equation:
q = mcΔT
where:
- q is the heat transferred (energy released) during combustion in Joules
- m is the mass of the substance burned in grams
- c is the specific heat capacity of the calorimeter (assumed to be constant)
- ΔT is the change in temperature of the calorimeter in degrees Celsius
First, let's calculate the heat transferred during the combustion of salicylic acid:
q1 = mcΔT
= (0.1182 g)(21.90 kJ/g)(2.84°C)
= 0.7091 kJ
Next, let's calculate the heat transferred during the combustion of the unknown substance:
q2 = mcΔT
= (0.2086 g)(c)(3.50°C)
Now, since the same calorimeter is used for both combustion reactions, we can assume that the specific heat capacity (c) remains constant. Therefore, the expression for q2 can be rewritten as:
q2 = (0.2086 g)(c)(3.50°C)
= 0.7261 g°C (c)
To find the energy of combustion per unit mass of the unknown substance, we need to compare the heat transferred in the two reactions:
(q2 / m2) = (q1 / m1)
where:
- (q2 / m2) is the energy of combustion per unit mass of the unknown substance
- m1 is the mass of the known substance burned (0.1182 g)
- m2 is the mass of the unknown substance burned (0.2086 g)
- q1 is the heat transferred during the combustion of the known substance
Solving for (q2 / m2):
(q2 / m2) = (q1 / m1)
0.7261 g°C (c) / 0.2086 g = 0.7091 kJ / 0.1182 g
Simplifying:
(c) / 0.2086 g = (0.7091 kJ / 0.1182 g) / 0.7261 g°C
c = [(0.7091 kJ / 0.1182 g) / 0.7261 g°C] * 0.2086 g
Finally, substitute the given values to find the energy of combustion per unit mass of the unknown substance:
(q2 / m2) = c
= [(0.7091 kJ / 0.1182 g) / 0.7261 g°C] * 0.2086 g
≈ 11.24 kJ/g
Therefore, the energy of combustion per unit mass of the unknown substance is approximately 11.24 kJ/g.