Parameters
Reaction Order
Rate constant k
0.100
Units: M/s (0th) · s⁻¹ (1st) · M⁻¹s⁻¹ (2nd)
Initial conc. [A]₀
1.000 M
Time range t_max
50.0 s
Read conc. at t*
25.0 s
—
Half-life t₁/₂ [s]
—
Initial rate v₀ [M/s]
—
[A](t*) [M]
—
k(T_ref)
Concentration [A](t) vs Time
ln k vs 1/T (Arrhenius Plot)
Theory
1st order: $[A]=[A]_0 e^{-kt}$, $t_{1/2}=\dfrac{\ln 2}{k}$
0th order: $[A]=[A]_0-kt$, $t_{1/2}=\dfrac{[A]_0}{2k}$
2nd order: $\dfrac{1}{[A]}=\dfrac{1}{[A]_0}+kt$, $t_{1/2}=\dfrac{1}{k[A]_0}$
Arrhenius equation:
$$k = A\,e^{-E_a/RT},\quad \ln k = \ln A - \frac{E_a}{R}\cdot\frac{1}{T}$$Slope $= -E_a/R$ — activation energy from the Arrhenius plot slope.
Applications: Optimal temperature design for chemical reactors (CSTR/PFR), pharmaceutical shelf-life and degradation rate prediction, polymer thermal degradation analysis (applying Arrhenius to TGA/DSC data).