Thermodynamics Question 3
Question 3 - 25 January - Shift 2
$28.0 L$ of $CO_2$ is produced on complete combustion of $16.8 L$ gaseous mixture of ethene and methane at $25^{\circ} C$ and $1 atm$. Heat evolved during the combustion process is_________________$kJ$.
Given : $\Delta H_C(CH_4)=-900 kJ mol^{-1}$
$\Delta H_C(C_2 H_4)=-1400 kJ mol^{-1}$
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Answer: (925)
Solution:
Formula: Thermochemical Reaction
Let, Volume of $C_2 H_4$ is $x$ litre
$ C_2 H_4+3 O_2 \to 2 CO_2+2 H_2 O $
Initial $\qquad\qquad x$
$ \begin{aligned} &\text{Final}\quad \qquad -\qquad 2 x \\ & CH_4+2 O_2 \to CO_2+2 H_2 O \end{aligned} $
Initial $\qquad(16.8-x)$
Final $\quad\qquad-$ $\quad\qquad(16.8-x)$
Total volume of $CO_2=2 x+16.8-x$
$ \begin{matrix} \Rightarrow & 28=16.8+x \\ \text{ } & x=11.2 \text{ L } \end{matrix} $
$n _{CH_4}=\frac{PV}{RT}=\frac{1 \times 5.6}{0.082 \times 298}=0.229$ mole
$n _{C_2 H_2}=\frac{11.2}{0.082 \times 298}=0.458$ mole
$\therefore$ Heat evolved $=0.229 \times 900+0.458 \times 1400$
$ \begin{aligned} & =206.1+641.2 \\ & =847.3 \text{kJ} \end{aligned} $
