Answer to Question #92421 in Chemistry for Tj

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