Second Order Reaction (One Reactant)

📊 intermediate

$$\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt$$

Reciprocal concentration increases linearly for second-order reaction.

Variables & Units

$[A]_t$

Concentration at time $t$

Unit: $\text{mol/L}$

$[A]_0$

Initial concentration

Unit: $\text{mol/L}$

$k$

Rate constant

Unit: $\text{L/(mol·s)}$

$t$

Time

Unit: $\text{s}$

Key Information

📐 Derived From

$d[A]/dt = -k[A]^2$

💡 Example

$[A]_0 = 0.5\,\text{M}$, $k=0.2\,\text{L/(mol·s)}$, $t=10\,\text{s}$: $1/[A] = 1/0.5 + 0.2\times10 = 2 + 2 = 4$, so $[A] = 0.25\,\text{M}$.

🔧 Applications

Dimerization reactions, enzyme kinetics (special cases)

⚠️ Constraints

Single reactant or equal initial concentrations

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