Answer to Question #171273 in General Chemistry for Emie

Question

Suppose a boil water notice is sent out advising all residents in the area to boil their water before drinking it or using it for cooking. You need to boil 11.5 L

11.5 L of water using your natural gas (primarily methane) stove. What volume of natural gas is needed to boil the water if only 17.1%

17.1% of the heat generated goes towards heating the water. Assume the density of methane is 0.668 g/L

0.668 g/L, the density of water is 1.00 g/mL

1.00 g/mL, and that the water has an initial temperature of 21.0 °C

21.0 °C. Enthalpy of formation values can be found in this table. Assume that gaseous water is formed in the combustion of methane.

Answer 1

Energy required for boiling of $11.5 L$ of water:

$1. \$ Energy required to increase it's temperature from $21\degree C\to100\degree C$

$2. \$ Energy required for boiling(Latent heat of evaporation)

$=mC(T_2-T_1)+mL_v=$ $11.5 \times 4.184\times (100-21)+11.5\times 2256=$ $29745.16J$

Let $V$ be the volume of methane required,

Mass of methane will be$=d\times V=0.668V g$ (where d is the density)

Calorific value of methane$=55KJ/g$

$17.1$ % of Total energy of methane $=$ $29745.16J$

$\implies \frac{17.1}{100}\times 55000\times 0.668\times V=29745.16J$

$V=4.73L$

$V=4.73L$