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Balancing Chemical Equations by Partial Equation Method

A natural gas...

Question

A natural gas may be assumed to be a mixture of methane and ethane only. On complete combustion of $10$ litre of gas at STP, the heat evolved was $474.6 k J$ . Assuming $Δ H_{c o m b} {C H}_{4} = - 894 k J {m o l}^{- 1}$ and $Δ H_{c o m b} C_{2} H_{6} = - 1500 k J$ .
Calculate the percentage composition of the mixture by volume.

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Solution

$x l i t r e ⟶ {C H}_{4}$ ; mole of ${C H}_{4} = x / 22.4$
$(10 - x) l i t r e ⟶ C_{2} H_{6}$ ; mole of $C_{2} H_{6} = (10 - x) / 22.4$
Heat evolved $= \frac{x}{22.4} \times 894 + \frac{(10 - x)}{22.4} \times 1500$
$474.6 = \frac{x}{22.4} \times 894 + \frac{(10 - x)}{22.4} \times 1500$
$x = 0.745$ , % ${C H}_{4} = 74.5$ %

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