Q15. natural gas burns in air to form carbon dioxide and water to releasing heat. cha(g) o2 (g) co2 g) h20 (g) ah 802.3 kj what minimum mass of ch4 is required to heat 55 g of water by 25 °c? (assume 100% heating efficiency. c) 115 g a) 0.115 g b) 2.25 x 103 g d) 8.70 g

a) 0.115 g

Explanation:

The balanced reaction is:

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g)

To heat 55g of water, the energy in form of heat necessary can be calculated by:

Q = mcΔT

where Q is the heat, m is the mass, c is the specific heat (for water, c = 4.18 J/gºC), and ΔT is the variation of the temperature, which is 25ºC, so:

Q = 55x4.18x25

Q = 5747.5 J = 5.7475 kJ

So, for the reaction, 1 mol of CH₄ releases 802.3 kJ, so to release 5.7475 kJ will be necessary:

1 mol 802.3 kJ

x 5.7475 kJ

By a simple direct three rule:

802.3x = 5.7475

x = 7.164x10⁻³mol

The molar mass of CH₄ is : 12 (of C) + 4x1 (of H) = 16 g/mol

The mass is equal to the number of moles multiplied by molar mass, the:

m = 7.164x10⁻³x16

m = 0.115 g

the dependant variable is spilled water

the independent is the heat