Lesson 1 of 11 · 7 min

Rate of a reaction

NCERT §3.1

The syringe takes 10 minutes to collect its first 40 mL of oxygen, but the next 40 mL takes forever. The reaction and the temperature stay the same, so why does it keep slowing down?

The story this chapter follows: The chemistry club's rate week

The school chemistry club spends a week timing reactions at 25 °C. Their main rig is a conical flask holding 50 mL of 0.13 M hydrogen peroxide with enough potassium iodide to make it 0.020 M in I⁻, sealed to a gas syringe that fills with oxygen: 40 mL after 10 minutes, 60 mL after 20, and close to 80 mL at the end. Beside it stand two jars of acidified permanganate with oxalic acid, one cool and one warm.

The lesson in notes

In short

Rate is the change in concentration of a reactant or product per unit time. Concentration is in mol L⁻¹ and time in s, min or h, so rate has units such as mol L⁻¹ s⁻¹; for gases, pressure in atm can replace concentration, giving atm s⁻¹.

For R → P, rate = −Δ[R]/Δt = +Δ[P]/Δt. The minus sign makes the rate positive, because [R] falls.

Average rate is the change over a finite interval. It hides the fact that the rate itself changes during that interval, usually falling as reactants are used up.

Instantaneous rate is the limit as Δt → 0: r = −d[R]/dt = d[P]/dt. On a concentration-time graph it is the slope of the tangent at that moment.

When coefficients differ, divide each rate of change by its coefficient so that every species gives the same number. For 2HI → H₂ + I₂: rate = −½ d[HI]/dt = d[H₂]/dt = d[I₂]/dt.

For 2N₂O₅ → 4NO₂ + O₂, rate = −½ Δ[N₂O₅]/Δt = ¼ Δ[NO₂]/Δt = Δ[O₂]/Δt. If [N₂O₅] falls from 2.33 to 2.08 mol L⁻¹ in 184 min, the reaction rate is ½ × 0.25/184 = 6.79 × 10⁻⁴ mol L⁻¹ min⁻¹, and NO₂ forms at four times that, 2.72 × 10⁻³ mol L⁻¹ min⁻¹.

Rates span a huge range: ionic precipitation (such as AgCl from Ag⁺ and Cl⁻) is almost instantaneous, the inversion of cane sugar and hydrolysis of starch go at a moderate pace, and the rusting of iron in moist air is very slow.