Answer to Question #97164 in General Chemistry for Dee

Question #97164
You need to boil 12.5 L of water using your natrual gas (primarily methane) stove. What volume of natural gas is needed to boil the water if only 15.6% of the heat generated goes towards heating the water. Assume the density of methane is 0.660g/L , the density of water is 1.00 g/mL , and that the water has an initial temperature of 23.4 °C
1
Expert's answer
2019-10-23T07:01:21-0400

Energy required for boiling of "12.5 L" of water:

"1. \\" Energy required to increase it's temperature from "23.4\\degree C\\to100\\degree C"

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

"=mC(T_2-T_1)+mL_v=" "12.5 \\times 4.184\\times (100-23.4)+12.5\\times 2256=" "32206.18KJ"

Let "V" be the volume of methane required,

Mass of methane will be"=d\\times V=0.66V g" (where d is the density)

Calorific value of methane"=55KJ\/g"

"15.6" % of Total energy of methane "=" "32206.18 KJ"

"\\implies \\frac{15.6}{100}\\times 55\\times 0.66\\times V=32206.18"

"V=5687.32 L"


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