How many liters of CH4(g), measured at 23.0 ∘C and 764 mmHg , must be burned to provide the heat needed to vaporize 3.86 L of water a...?

2016-07-29 4:34 pm
更新1:

at 100 ∘C? ΔHcombustion=−8.90×102kJmol−1CH4. For H2O(l) at 100 ∘C, d=0.958gcm−3 and ΔHvap=40.7kJmol−1.

回答 (1)

2016-07-29 6:00 pm
Molar mass of H₂O (water) = (1.006×2 + 16.00) g mol⁻¹ = 18.02 g mol⁻¹
Molar mass of CH₄ = (12.01 + 1.008×4) g mol⁻¹ = 16.04 g mol⁻¹

Heat absorbed by water (in kJ) = [(3860 cm³) × (0.958 g cm⁻³) / (18.02 g mol⁻¹)] × (40.7 kJ mol⁻¹)
Heat released in burning CH₄ (in kJ) = [n(CH₄) mol] × (8.90 × 10² kJ mol⁻¹)

Heat released in burning CH₄ = Heat absorbed by water
n(CH₄) × (8.90 × 10²) = [3860 × 0.958 / 18.02] × 40.7
n(CH₄) = 9.38 mol

For the CH₄ gas :
P = 764 mmHg
V = ? L
n = 9.38 mol
R = 62.36 mmHg L mol⁻¹ K⁻¹
T = (273.2 + 23.0) K = 296.2 K

PV = nRT
V = nRT/P

Volume of CH₄ burned = 9.38 × 62.36 × 296.2 / 764 = 227 L


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