The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is
2K₂Cr₂O₇ + 8H₂SO₄ + 3C₂H₆O → 2Cr₂(SO₄)₃ + 3C₂H₄O₂ + 2K₂SO₄ + 11H₂O
If the rate of appearance of Cr₂(SO₄)₃ is 2.67 mol min⁻¹ at a particular time, the rate of disappearance of C₂H₆O at the same time is _____________ mol min⁻¹. (Nearest integer)

Solution

Chemistry ma’am · 3 steps

Divide each rate by its coefficient and the two sides must match. Then just read off ethanol's rate.

1. One common rate. The rate of a reaction is the same whichever species you track, once you divide that species' rate by its coefficient in the balanced equation. Here Cr₂(SO₄)₃ has coefficient 2 and C₂H₆O has coefficient 3.

   -1/3d[C₂H₆O]/dt = 1/2d[Cr₂(SO₄)₃]/dt

2. Put in numbers. Rate of disappearance of C₂H₆O = 3/2 × 2.67 = 4.005 mol min⁻¹.
3. So. Three ethanol molecules are used up for every two Cr₂(SO₄)₃ formed, so ethanol disappears faster. The answer is 4.

The common slip: 2. Multiplying by 2/3 instead of 3/2 gives 1.78, which rounds to 2. Check that the species with the larger coefficient has the larger rate.

The idea to keep. Rate of one species divided by its stoichiometric coefficient is the same for every species. The species with the bigger coefficient always changes faster.

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