Consider the reaction represented by the following equation: xCH$_3$OH + yO$_2$ → 2CO$_2$ + zH$_2$O. The values of x,y and z respectively, are

Analyze the question: We need to balance the combustion of methanol, xCH₃OH + yO₂ → 2CO₂ + zH₂O, and find x, y and z.

Concept: To balance an equation, the number of atoms of each element must be the same on both sides. Start with carbon, then hydrogen, and balance oxygen last.

Step-by-step solution:

1. Carbon: The right side has 2 CO₂, so there are 2 C atoms. Each CH₃OH has 1 C, so x = 2.

2. Hydrogen: Each CH₃OH has 4 H atoms (3 in CH₃ and 1 in OH). So 2 CH₃OH gives 8 H atoms. Each H₂O has 2 H, so 2z = 8 and z = 4.

3. Oxygen: • Right side: 2 CO₂ gives 4 O, and 4 H₂O gives 4 O, so the total is 8 O. • Left side: 2 CH₃OH gives 2 O, and y O₂ gives 2y O, so the total is 2 + 2y. • Setting 2 + 2y = 8 gives 2y = 6, so y = 3.

Balanced equation: 2CH₃OH + 3O₂ → 2CO₂ + 4H₂O

Check:

• C: 2 = 2 ✓
• H: 8 = 8 ✓
• O: 2 + 6 = 8 and 4 + 4 = 8 ✓

So x, y and z are 2, 3 and 4 respectively.

Exam tip: Balance in the order C → H → O. Oxygen usually appears in several compounds, so leaving it for last makes it easy. You can also test the options quickly: since the equation shows 2CO₂, x must be 2, which eliminates C and D immediately. Then check hydrogen: 8 H needs z = 4, which leaves only A.