Question

The combustion of toluene has a δerxn of −3.91 × 103kj/mol. when 1.55 g of toluene (c7h8) undergoes combustion in a bomb calorimeter, the temperature rises from 23.02 ∘c to 37.92 ∘c. find the heat capacity of the bomb calorimeter.

Answer 1

Answer: The heat capacity of the bomb calorimeter is $2.84 kJ/g^oC$.

Explanation:

$\Delta H_{reaction}=-3.91\times 10^3 kJ/mol=-3.91\times 10^6 J/mol(1kJ=1000J)$

Given mass of toluene = 1.55 g

Number of moles of Toluene:

$=\frac{\text{Given mass of toluene}}{\text{Molecular mass of toluene}}=\frac{1.55}{92.14 g/mol}=0.0168 moles$

Energy required by 0.0168 moles of toluene=$\Delta H_{reaction}\times 0.0168 moles=-3.91\times 10^6 J/mol\times 0.0168 mol=-0.065688\times 10^6 J$

Since heat released on combustion of 0.0168 moles toluene, this heat will get absorbed by the bomb calorimeter ,then (Q) will be:

$Q=0.065688\times 10^6 J$

$\Delta T= 37.92^oC-23.02^oC=14.9^oC$

$Q=mc\Delta T=0.065688\times 10^6 J=1.55 g\times c \times (14.9^oC)$

$c=2.84\times 10^3 J/g^oC=2.84 kJ/g^oC$

The heat capacity of the bomb calorimeter is $2.84 kJ/g^oC$.

Answer 2

2.84 kJ/g⁰C is the heat capacity of the bomb calorimeter where combustion of toluene takes place.

How we calculate the specific heat capacity?

Specific heat capacity can be calculated by using the below formula:

Q = mcΔT, where

Q = heat absorbed or released

m = mass

ΔT = change in temperature

For this question first we have to calculate the Q, and this can be calculated as follow:

Given ΔH for combustion of toluene = −3.91 × 10³kj/mol = −3.91×10⁶J/mol

Given mass of to toluene = 1.55g

Moles of toluene can be calculated as : n = W/M, where

W = given weight

M = molar mass

n = 1.55g / 92.14gmole = 0.0168moles

Energy required by 0.0168 moles of toluene = 0.0168×(−3.91×10⁶) = -0.06568 × 10⁶J

And this combustion energy will be absorbed by the bomb calorimeter.

Now specific heat capacity can be calculated by putting all values in the above equation as:

c = Q / mΔT,

c = 0.06568 × 10⁶J / 1.55g × (37.92⁰C - 23.02⁰C)

c = 2.84 × 10³J/g⁰C = 2.84 kJ/g⁰C

Hence, the heat capacity of bomb calorimeter is 2.84 kJ/g⁰C.

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