Answer to Question #171273 in General Chemistry for Emie

Question #171273

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.


1
Expert's answer
2021-03-15T09:26:35-0400

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"

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