Order finder

The first line, “t (s), [A] (M)”, was read as column titles and skipped.

All three plots

The working

Intermediate values are carried to six significant figures; results are rounded to three at the end.

1. Each plot was fitted with a least-squares straight line through all 6 readings:

   Plot	Slope	Intercept	R2
   [A] vs t	−1.75657 × 10−4	0.0841623	0.8909
   ln [A] vs t	−5.00032 × 10−3	−2.30258	1.0000
   1/[A] vs t	0.21402	−4.46583	0.8910

2. The straightest line (highest R²) is ln [A] against t, the first order plot: ln [A] = ln [A]₀ − kt.
3. For first order the slope is −k, so k = −(−5.00032 × 10⁻³) = 5.00 × 10⁻³ s⁻¹.
4. The intercept gives [A]₀: [A]₀ = e^intercept = e^−2.30258 = 0.100 M.
5. Half-life: t_½ = ln 2 / k = 0.693147 / (5.00032 × 10⁻³) = 139 s.
6. [A] at t = 750 s: ln [A] = ln [A]₀ − kt = −2.30258 − (5.00032 × 10⁻³ × 750) = −2.30258 − 3.75024 = −6.05282, so [A] = e^−6.05282 = 2.35 × 10⁻³ M.
7. Time to [A] = 0.001 M: t = ln([A]₀/[A]) / k = ln(0.100001 / 0.001) / (5.00032 × 10⁻³) = 4.60518 / (5.00032 × 10⁻³) = 921 s.

The 6 readings as used

t (s)	[A] (M)	ln [A]	1/[A] (M−1)
0	0.1000	−2.30259	10
100	0.06065	−2.80264	16.488
200	0.03679	−3.30253	27.1813
300	0.02231	−3.80272	44.8229
400	0.01353	−4.30285	73.9098
500	8.208 × 10−3	−4.80265	121.832