First let us calculate heat required to raise the temperature
Q = mc∆T
Q = heat energy (Joules, J), m = mass of a substance (g)
c = specific heat (units J/g∙oC), ∆ is a symbol meaning "the change in"
∆T = change in temperature (oC Celcius)
Q = 50 g x 4.184 J/g∙oC x 24 oC
Q = 5020.8 Joules or 5.020 Kilo Joules
One mole of Methane will release 802.3 Kilo joules of heat
Moles of Methane required to release 5.020 Kilo joules of heat = 5.020 /802.3 = 0.00625 Moles
molar mass of methane = 16 g/mol
Mass of Methane required to release 5.020 Kilo joules of heat = 0.00625 Mole x 16 g/mol = 0.1 gm
Hence 0.1 gm of methane is required to raise the temperature of 50 gm of water by 24oC
Option B is correct answer
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