Question

What mass of methane (CH4(g)) needs to be burned to heat 300 mL of water from 23.0 oC to the boiling point (98.0 oC)? (ΔHcombustion = -639 kJ /mol ; specific heat of water = 4.18 J/goC)

(Please note that you must include units throughout all of your calculations and provide your answer in scientific notation to the correct number of significant digits.)

Answer 1

The heat that is required to heat water is:

Q₁ = m_water × c_p × (T₂ - T₁),

where m_water - mass of water, c_p - specific heat of water, T₂ - final temperature, T₁ - initial temperature.

The process of methane burning releases the heat:

Q₂ = ΔH_comb × N = ΔH_comb × (m_methane / Mr_methane)

where ΔH_comb - compustion enthalpy, N - number of moles, m - mass of methane, Mr - molecular weight of methane.

As Q₁ = Q₂:

ΔH_comb × (m_methane / Mr_methane) = m_water × c_p × (T₂ - T₁).

From here:

m_methane = [Mr_methane × m_water × c_p × (T₂ - T₁)] / ΔH_comb

As Mr_methane = 16 g/mol, m_water = 300 g, c_p = 4.18 J/g°C, T₂ = 98°C, T₁ = 23°C, ΔH_comb = - 639 kJ /mol = 639 × 10³ J/mol:

m_methane = [16 g/mol × 300 g × 4.18 J/g°C (98°C - 23°C)] / 639 × 10³ J/mol = 2.35 g

Answer: 2.35 g of methane