Thermodynamics and Thermochemistry - Result Question 2
2. The difference between $\Delta H$ and $\Delta U(\Delta H-\Delta U)$, when the combustion of one mole of heptane $(l)$ is carried out at a temperature $T$, is equal to
(2019 Main, 10 April II)
(a) $-4 R T$
(b) $3 R T$
(c) $4 R T$
(d) $-3 R T$
Show Answer
Answer:
Correct Answer: 2. (a)
Solution:
Key Idea: The relation between $ \Delta H \text { and } \Delta U \text { is }$
$ \qquad \Delta H=\Delta U+\Delta n _g R T$
$\text { where, } \quad \Delta n _g=\Sigma n _p-\Sigma n _R$
$=$ number of moles of gaseous products - number of moles of gaseous reactants.
The general combustion reaction of a hydrocarbon is as follows :
$ C _x H _y+\left(x+\frac{y}{4}\right) O _2 \longrightarrow x CO _2+\frac{y}{2} H _2 O $
For heptane, $x=7, y=16$
$\Rightarrow C _7 H _{16}(l)+11 O _2(g) \longrightarrow 7 CO _2(g)+8 H _2 O(l) $
$\therefore \Delta n _g=7-11=-4$
Now, from the principle of thermochemistry,
$ \begin{aligned} \Delta H & =\Delta U+\Delta n _g R T \\ \Rightarrow \quad \Delta H-\Delta U & =\Delta n _g R T=-4 R T \end{aligned} $
BETA
