When one mole of a hydrocarbon C _ a H _ b undergoes complete combustion, it requires 7.5 moles of O ₂ and results in the production of 6 moles of CO ₂ . Calculate the values of a and b .

Step-by-step solution

The combustion reaction of a hydrocarbon C_ a H_ b is given by the equation: C_ a H_ b + (a + b 4 )O₂ aCO₂ + b 2 H₂O Given that 6 moles of CO₂ are produced from 1 mole of hydrocarbon, we have a = 6 . Given that 7.5 moles of O₂ are required for complete combustion, we have the stoichiometric coefficient for oxygen: a + b 4 = 7.5 Substituting a = 6 into the equation: 6 + b 4 = 7.5 b 4 = 7.5 - 6 = 1.5 b = 1.5 4 = 6 Therefore, a = 6 and b = 6 . Answer: a=6 and b=6