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Choose the Best Answer · Q18

Q.When 15.68 litres of a gas mixture of methane and propane are fully combusted at 0∘0^\circC and 1 atmosphere, 32 litres of oxygen at the same temperature and pressure are consumed. The amount of heat released from this combustion in kJ is (ΔHC(CH4)=−890\Delta H_C(CH_4) = -890 kJ mol−1^{-1} and ΔHC(C3H8)=−2220\Delta H_C(C_3H_8) = -2220 kJ mol−1^{-1})

(a) – 889 kJ
(b) – 1390 kJ
(c) – 3180 kJ
(d) – 632.68 kJ
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Step 1. Let xx = volume CH4_4, yy = volume C3_3H8_8 in the 15.68 L mixture, so x+y=15.68x+y=15.68. Combustion needs 2 mol O2_2 per mol CH4_4 and 5 mol O2_2 per mol C3_3H8_8; at the same T,PT,P volume ratios equal mole ratios, so 2x+5y=322x+5y=32.

Step 2. Substituting x=15.68−yx=15.68-y: 2(15.68−y)+5y=32⇒31.36+3y=32⇒y=0.21332(15.68-y)+5y=32 \Rightarrow 31.36+3y=32 \Rightarrow y=0.2133 L, so x=15.4667x=15.4667 L.

Step 3. At 0∘0^\circC, 1 atm, molar volume =22.4=22.4 L mol−1^{-1}: moles CH4=15.4667/22.4=0.6905_4=15.4667/22.4=0.6905 mol; moles C3_3H8=0.2133/22.4=0.00952_8=0.2133/22.4=0.00952 mol. …

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