JEE Main 2020 · 3 September · evening · Single correct · +4 / −1

For the reaction
2A + 3B + 3/2C → 3P, which statement is correct ?

  1. (a) dn_A/dt = dn_B/dt = dn_C/dt
  2. (b) dn_A/dt = 2/3dn_B/dt = 3/4dn_C/dt
  3. (c) dn_A/dt = 3/2dn_B/dt = 3/4dn_C/dt
  4. (d) dn_A/dt = 2/3dn_B/dt = 4/3dn_C/dt
Answer and solution

Answer (d) dn_A/dt = 2/3dn_B/dt = 4/3dn_C/dt

Solution

Chemistry ma’am · 3 steps

Divide each rate by its own coefficient, set them equal, then solve for dn_A/dt.

  1. One common rate. Each species is used up at a rate set by its coefficient. Dividing each dn/dt by its coefficient gives the same number for all of them. A, B and C are all reactants, so all three derivatives carry the same negative sign.

    -1/2dn_A/dt = -1/3dn_B/dt = -1/(3/2)dn_C/dt = -2/3dn_C/dt

  2. Isolate the A rate. Multiply every term by -2 so that dn_A/dt stands alone. The B term becomes 2/3dn_B/dt. The C term becomes 2 × 2/3 = 4/3, giving 4/3dn_C/dt.
  3. So. dn_A/dt = 2/3dn_B/dt = 4/3dn_C/dt, which is option (d).

The idea to keep. Write the common rate as 1/νdn/dt for every species, then rearrange. With a fractional coefficient like 3/2, dividing by it means multiplying by 2/3.

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

Study Mole Concept & Stoichiometry

Asked about 210 times in JEE Main since 2020. This question is from 2020.