For the reaction A → products.
The concentration of A at 10 minutes is _________ × 10⁻³ mol L⁻¹ (nearest integer). The reaction was started with 2.5 mol L⁻¹ of A .

Solution

Chemistry ma’am · 4 steps

Half-life rising in step with [A]₀ means zero order, so read k off the slope.

1. Identify the order. The half-life grows in direct proportion to the starting concentration. Only a zero-order reaction does this, where t_(1/2) = [A]₀/2k.
2. Rate constant from slope. A plot of t_(1/2) against [A]₀ has slope 1/2k. So 1/2k = 76.92 min L mol⁻¹, which gives k = 1/153.84 = 6.5 × 10⁻³ mol L⁻¹ min⁻¹.

   [A]ₜ = [A]₀ - kt

3. Put in numbers. In 10 minutes A falls by kt = 6.5 × 10⁻³ × 10 = 0.065 mol L⁻¹. So [A] = 2.5 - 0.065 = 2.435 mol L⁻¹.
4. So. [A] = 2435 × 10⁻³ mol L⁻¹, so the answer is 2435.

The common slip: 2370. Taking the slope as 1/k and missing the factor of 2 gives k = 0.013 mol L⁻¹ min⁻¹ and [A] = 2.37 mol L⁻¹, which is 2370 instead of 2435.

The idea to keep. If t_(1/2) grows in proportion to [A]₀, it is zero order. If it stays fixed, it is first order. For zero order the slope of t_(1/2) against [A]₀ is 1/2k, not 1/k.

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