Although the heat energy change (Q) tells us the amount of heat energy transferred to or absorbed from the surroundings, it does not tell us the amount of heat energy absorbed or released for every mole of the substance which reacts.
The amount of heat energy absorbed or released for every mole of the substance which reacts is known as the molar enthalpy change and is represented as â–³H.
â–³H cannot be measured directly but can be calculated from the heat energy change using the expression:
![\[\nabla H = -\frac{Q}{n} \]](https://online-learning-college.com/wp-content/ql-cache/quicklatex.com-19a2f8e637f505d9f949d033b9f63447_l3.png "Rendered by QuickLaTeX.com")
where:
â–³H is the molar enthalpy change (kJ/mol)
Q is the heat energy change (J)
n is the number of moles of the substance that reacted (mol)
The number of moles of the substance that reacted can be calculated using the equation:
![\[\text{Number of moles (mol)} \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]](https://online-learning-college.com/wp-content/ql-cache/quicklatex.com-380aebc1103c21ccb3dbb431e45eec6d_l3.png "Rendered by QuickLaTeX.com")
Notice that the units for â–³H and Q are different. DH is given in kJ/mol and Q is given in J. To calculate the value for â–³H, the value for Q in J must be converted in kJ by dividing the value by 1000.
In worked example 1 from the previous section, we calculated that 12810J of heat energy was transferred to the water from the combustion of the ethanol in the spirit burner.
By adding some detail about the amount of ethanol that was burned we can calculate the molar enthalpy change for the combustion of ethanol, as shown in the next example.
Example
The mass of the ethanol, spirit burner and the lid before heating was measured as 68.75g. After heating the mass was measured again and recorded as 68.15g. The heat energy change for the reaction was 12810J. Calculate the molar enthalpy change for the combustion of ethanol.
To calculate the number of moles of ethanol burned, we firstly need to calculate the mass of ethanol used in the reaction. The masses of the spirit burner before and after heating differ due to the ethanol undergoing a combustion reaction and reacting with oxygen to produce carbon dioxide and water. The difference in mass is therefore the mass of ethanol burned. To calculate the mass of ethanol burned therefore we subtract the final mass from the starting mass.
0.6g of ethanol was burned in this combustion reaction. Therefore, 0.6g of fuel releases 12810 joules of energy. We can now calculate the number of moles of ethanol burned using the equation:
![\[\text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]](https://online-learning-college.com/wp-content/ql-cache/quicklatex.com-664971c5387ade3d515e83a9d65c806c_l3.png "Rendered by QuickLaTeX.com")
The molar mass of a substance is calculated by adding up the relative atomic masses of all elements in the substance.
The chemical formula of ethanol is C2H5OH. The molar mass for ethanol is calculated therefore as (2 x 12) + (5 x 1) + 16 + 1 = 46.0g/mol.
The number of moles of ethanol burned is therefore:
![\[\text{Number of moles} = \frac{0.6}{46.0} = 0.0130 mols \]](https://online-learning-college.com/wp-content/ql-cache/quicklatex.com-a118c96898f8dcd5f1b5d4dd7c7cc03f_l3.png "Rendered by QuickLaTeX.com")
The molar enthalpy change tells us the amount of energy released by 1 mole of the substance. From our calculations we know that 0.0130 moles of ethanol burned to produced 12810J of energy.
To calculate the value for â–³H, the value for Q in J must be converted in kJ by dividing the value by 1000. Therefore, 0.0130 moles of ethanol burned to produce 12.810kJ of energy. We can now calculate the molar enthalpy change for the combustion of ethanol using the expression:
![\[\nabla H = \frac{-Q}{n}\]](https://online-learning-college.com/wp-content/ql-cache/quicklatex.com-9cde03fd36750a36236cdd23da27c58e_l3.png "Rendered by QuickLaTeX.com")
![\[\nabla H = \frac{-12.810kJ}{0.0130mol}\]](https://online-learning-college.com/wp-content/ql-cache/quicklatex.com-5a23fdc131ee6b651644163e26e2e7cf_l3.png "Rendered by QuickLaTeX.com")
![\[\nabla H = \frac{-985.4kJ}{mol}\]](https://online-learning-college.com/wp-content/ql-cache/quicklatex.com-f9a048c9c1c9b70acab83561276b2287_l3.png "Rendered by QuickLaTeX.com")
The accepted data book value for the combustion of ethanol is -1367kJ/mol. Our calculated value is much lower than this due to the loss of heat energy to the surroundings such as the beaker or the air, as well as incomplete combustion.
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