The hydrocarbon (X) with molar mass 80 g mol⁻¹ and 90% carbon has _______ degree of unsaturation.

Solution

Chemistry ma’am · 3 steps

Turn the percentage into grams of C and H first, find the formula, then count the missing hydrogens.

1. Find the formula. In 80 g of X, carbon is 0.90 × 80 = 72 g, which is 72 ÷ 12 = 6 mol of C. The remaining 8 g is hydrogen, which is 8 ÷ 1 = 8 mol of H. So X is C₆H₈.
2. Compare with saturated. A saturated open-chain hydrocarbon with 6 carbons is C₆H₁₄ (CₙH₂ₙ₊₂). Every ring or every π bond removes 2 hydrogens from that count.

   DoU = ((2C + 2) - H)/2 = ((2 × 6 + 2) - 8)/2 = 6/2 = 3

3. So. C₆H₈ is short of C₆H₁₄ by 6 hydrogens, which is 3 pairs. Its degree of unsaturation is 3.

The common slip: 6. Stopping at the 6 missing hydrogens without dividing by 2 gives 6, not 3. Each ring or π bond removes two hydrogens.

The idea to keep. Degree of unsaturation counts pairs of hydrogens missing from CₙH₂ₙ₊₂. Each ring or π bond takes away one pair, so always divide the missing hydrogens by 2.

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