Question

Calculate the mass of methane that must be burned to provide enough heat to convert 320.0 g of water at 46.0°C into steam at 122.0°C. (Assume that the H2O produced in the combustion reaction is steam rather than liquid water.)

Answer 1

Water is heated from 46 ⁰C to 122⁰C

Energy needed to raise the temperature of 320 g water from 46⁰C to 100⁰C, will be

Q = m*s*t
where Q is heat energy, m is the mass of water, s is the specific heat (s for waster is 4.2 J/g ⁰C) and t is the temperature difference.

=> Q = 320 * 4.2 * (100-46)
=> Q = 72576 J

Energy required to get water to turn to steam = Mass X Specific latent heat of vaporization of water

= (320)(2260)
= 723200 J

Energy needed to get steam up to 122°C =
Q = m*s*t

= (320)(4.2)(22)
=29568 J

Total heat required = 72576 + 723200 + 29568 = 825344 J

for methane is 890 Kj/mol, Mol. Wt of methane is 16 g/mol
Heat produced per gram of methane = 890 / 16 = 55.625 kJ/g

So, mass of methane required = 825344 J /55.625 kJ/g = 14.84 g