Question

In a gobar gas plant, gobar gas is formed by bacterial fermentation if animal refuse. It mainly contains methane and its heat of combustion is $-809kJmo{l}^{-1}$ according to the following equation :
$C{H}_4+2O_2\to C{O}_2+2H_{2}O$ ; $\Delta H=-809kJ$
How much gobar gas would have to be produced per day for a small village of 50 families if it is assumed that each family requires 20,000 kJ of energy per day? The methane content in gobar gas is 80% by mass.

Answer 1

1 family - 20000 kJ - 1 day
5 family - 5 $\times$ 20000 kJ - 1 day
5 families - 100000 kJ - 1 day
$C{H}_4+O_2\to C{O}_2+H_{2}O;\Delta C=-809kJmo{l}^{-1}$
1 mol of $C{H}_4\to -809kJ$
$16g\to -809kJ$
gobar gas contains 80% of $C{H}_4$
809 of $C{H}_4\to 100g$ of gobar gas
$16g\to -80gkJ$
$809\to ?$
$=-\frac{80-809}{16}kJ$
100000 kJ $\to$ 1 day
$\frac{80\times 809}{16}kJ\to$ ?
$=\frac{\frac{80\times 809}{16}\times 1}{100000}$
$=\frac{80\times 809}{16\times 100000}=\frac{4045}{100000}$