S( g)+3/2 O₂( g) → SO₃( g)+2 x kcal ; SO₂( g)+1/2 O₂( g) → SO₃( g)+y kcal
The heat of formation of SO₂( g) is given by :

Solution

Chemistry ma’am · 3 steps

Write both heats as Δ H with a minus sign, then subtract the second reaction from the first.

1. Read the signs. Heat written on the product side is heat given out, so each reaction is exothermic. That means Δ H₁ = -2x kcal for forming SO₃ from S, and Δ H₂ = -y kcal for forming SO₃ from SO₂.
2. Build the target. The target is S + O₂ → SO₂. Take reaction 1 and subtract reaction 2. SO₃ cancels, 3/2 - 1/2 = 1 mole of O₂ stays on the left, and SO₂ moves to the right.

   Δ H_f(SO₂) = Δ H₁ - Δ H₂ = (-2x) - (-y) = y - 2x

3. So. The heat of formation of SO₂ is (y - 2x) kcal, which is option (c).

The idea to keep. Hess's law is just algebra on equations. Turn every heat term into a Δ H with its sign first, then add or subtract the reactions exactly as you add or subtract their Δ H values.

Answer from the NTA final answer key. Solution by PrepWiser.