Question

A bomb calorimeter has a heat capacity of 2.47 kj/k. when a 0.120-g sample of ethylene (c2h4) was burned in this calorimeter, the temperature increased by 2.44 k. calculate the enthalpy change per mole of ethylene combusted.

Answer 1

1,41 x 10³  kJ/mol

Further explanation

Given:

• A bomb calorimeter has a heat capacity of C = 2.47 kJ/K.
• A 0.120-g sample of ethylene (C₂H₄) was burned in this calorimeter.
• The temperature increased by ΔT = +2.44 K.

Question:

Calculate the enthalpy change per mole of ethylene combusted.

The Process:

Step-1: find out the amount of heat energy (Q) transferred

We will solve the problem with calorimetry calculations. We all see that the bomb calorimeter has a thermal (or thermal) capacity. During the sample was burned, there was an increase in temperature.

Q = heat capacity x temperature difference

$\boxed{ \  Q = C \  \Delta T \ }$

$\boxed{ \ Q = 2.47 \ \frac{kJ}{K} \times 2.44 \ K \ }$

Hence the amount of heat energy transferred in the reaction of the bomb calorimeter is 6.0268 kJ.

Step-2: calculate the number of moles of ethylene combusted

Molar mass of ethylene (C₂H₄) = (2 x 12.011) + (4 x 1.008) = 28.054.

Let us convert the number of grams of a sample of ethylene into moles.

$\boxed{ \ moles (n) = \frac{mass}{molar \ mass} \ }$

$\boxed{ \ moles (n) = \frac{0.120}{28.054} \ }$

We get $\boxed{ \ 4.277 \times 10^{-3} \ moles \ }$ of ethylene.

Step-3: calculate the enthalpy change per mole of ethylene combusted

$\boxed{ \ \Delta H = - \frac{heat \ transferred}{moles  \ of \ substance}\ \ } \rightarrow \boxed{ \ \Delta H = - \frac{Q}{n} \ }$

$\boxed{ \ \Delta H = - \frac{6.0268 \ kJ}{4.277 \times 10^{-3} \ moles} \ }$

Thus the enthalpy change per mole of ethylene combusted is $\boxed{ \ \Delta H = 1409.12 \ kJ/mol \ } \rightarrow \boxed{ \ \Delta H \approx 1,41 \times 10^3 \ kJ/mol \ }$

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Notes:

• The enthalpy change for a reaction can be measured experimentally by using a calorimeter.
• In a simple calorimeter all the heat evolved in exothermic reaction when is used to raise the temperature of a known mass of water (or heat capacity of a bomb calorimeter).
• For endothermic reactions the heat transferred from the water to the reaction can be calculated by measuring the lowering of temperature of a known mass of water (or heat capacity of a bomb calorimeter).  

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Answer 2

The enthalpy change per mole of ethylene combusted is 1401.63 kJ/mol.

The given parameters;

• heat capacity of the bomb, C = 2.47 kJ/k
• increase in temperature, Δt = 2.44 k
• mass of the ethylene sample = 0.12 g

The quantity of heat transferred to the calorimeter when the temperature was increased;

Q = CΔt

Q = (2.47)(2.44)

Q = 6.027 kJ

The number of moles of the ethylene is calculated as follows;

mass of ethylene = (12 x 2) + (1 x 4) = 28 g

$no \ of \ mole = \frac{0.12}{28} = 0.0043 \ mol$

The enthalpy change per mole of ethylene combusted is calculated as follows;

$\Delta H = \frac{6.027 \ kJ}{0.0043 \ mol} = 1401.62 \ kJ/mol$

Thus, the enthalpy change per mole of ethylene combusted is 1401.63 kJ/mol.

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