Question

The difference between $\Delta H\text{ and }\Delta \text{U (}\Delta \text{H-}\Delta U),$ when the contribution of one mole of heptane (1) is carried out at a temperature T, is equal to:
a.) 3RT
b.) -3RT
c.) -4RT
d.) 4RT

Answer 1

. The relation between the change in enthalpy and internal energy with the temperature of the system is $\Delta H=\Delta U+\Delta nRT$, one mole of heptane reacts with 11 mole of oxygen to produce 7 mole of carbon dioxide and water molecules. We have to calculate the difference in number of moles between the number of moles of reactant and the number of moles of products.

Complete step by step answer:
Given in the question:
One mole of heptane (1) is carried out at a temperature T
We have to calculate the difference between $\Delta H\text{ and }\Delta \text{U (}\Delta \text{H-}\Delta U),$
The reaction involved is mentioned below:
${{C}_{7}}{{H}_{16}}(l)+{{O}_{2}}(g)\to C{{O}_{2}}(g)+{{H}_{2}}O(l)$

And the balanced chemical reaction will be:
${{C}_{7}}{{H}_{16}}(l)+11{{O}_{2}}(g)\to 7C{{O}_{2}}(g)+8{{H}_{2}}O(l)$

Now we have to calculate the difference between the numbers of moles i.e. the difference between the number of moles of product to the number of moles of reactants.
$\Delta n={{n}_{p}}-{{n}_{r}}$
The total number of moles on reactant sides = 12
The total number of moles on product side = 7
The value of $\Delta n={{n}_{p}}-{{n}_{r}}$= $7-11$= -4
Put the value in the equation:
$\Delta H=\Delta U+\Delta nRT$
$\Delta H-\Delta U=-4RT$
So, the correct answer is “Option C”.

Note: Make sure that you put the value of temperature in kelvin units not in degree centigrade. We will need to put the value of the change in moles of gases during the reaction so it is important to balance the chemical reaction. The balanced reaction helps to correctly identify the number of moles which is most important for this question.