Chemical Kinetics Laboratory: Heterogeneous Reactions

Speed:

0s 300s

Time t = 0.0 s

Span:

Condition Set 1

Reference

Initial Concentration [B]₀: 1.00 M

Solution Volume V_B: 0.50 L

Temperature T: 25.0 °C

Surface Area of Solid A: 1.00x

Morphology: Coarse Pellets

k_eff

0.0131

r₀ (Initial)

0.0131 M/s

Max Yield C

0.250 mol

Condition Set 2

Comparative

Initial Concentration [B]₀: 1.00 M

Solution Volume V_B: 0.50 L

Temperature T: 40.0 °C

Surface Area of Solid A: 2.00x

Morphology: Fine Powder

k_eff

0.0624

r₀ (Initial)

0.0624 M/s

Max Yield C

0.250 mol

Physical Reactor Simulation Bubbling & Color Shift ∝ Rate & Concentration

Set 1 25.0°C

C: 0.00 mol

Set 2 40.0°C

C: 0.00 mol

Kinetic Charting Engine

Set 1 Current: 0.000 mol

Set 2 Current: 0.000 mol

Kinetic Target Challenge Game

Optimize Set 2 reaction conditions to meet specific product yield & kinetic targets under physical constraints.

Level 1: Yield Master Target: Product Yield

Produce at least 0.35 moles of C within 40 seconds using Set 2 parameters.

Target Time: 40 s

Target Amount C: ≥ 0.350 mol

Constraints: T ≤ 35°C, V_B ≤ 1.0L

Challenge Evaluation

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Set 2 Configuration Sliders

Molarity [B]₀ 1.0 M

Volume V_B 0.5 L

Temperature T (°C) 25 °C

Surface Area Factor 1.0x

Numerical Data Inspector

Time-series kinetic data sampled across simulation runtime.

Time (s)	Set 1 n_C (mol)	Set 1 [B] (M)	Set 1 Rate (M/s)	Set 2 n_C (mol)	Set 2 [B] (M)	Set 2 Rate (M/s)

Heterogeneous Chemical Kinetics Theory

Mathematical and physical foundations of the $A(s) + 2B(aq) \rightarrow C(aq)$ reaction.

1. Integrated Rate Law (2nd Order in B)

For the elementary step A(s) + 2B(aq) → C(aq) with rate law r = k_eff[B]²:

d[B] / dt = - 2 · k_eff · [B]²

Integrating from t = 0 to t yields:

[B](t) = [B]₀ / (1 + 2 · k_eff · [B]₀ · t)

The yield of product C in moles is:

n_C(t) = (k_eff · V_B · [B]₀² · t) / (1 + 2 · k_eff · [B]₀ · t)

2. Arrhenius Equation & Temperature

The rate constant k increases exponentially with absolute temperature T (K) according to the Arrhenius equation:

k_eff = A_pre · exp(-E_a / (R · T)) · SA_ratio

A_pre: Pre-exponential frequency factor ($10^6\text{ L/mol}\cdot\text{s}$)
E_a: Activation Energy ($45,000\text{ J/mol}$)
R: Universal Gas Constant ($8.314\text{ J/mol}\cdot\text{K}$)

3. Heterogeneous Surface Area Effect

Because Reactant A is a solid phase and Reactant B is aqueous, collisions can only occur at the solid-liquid interface.

Subdividing solid A into fine powders or nanoparticles dramatically increases the exposed surface area per unit mass, multiplying effective collisions and scaling $k_{\text{eff}}$ directly.

4. Second-Order Half-Life & Max Yield

Unlike 1st order reactions, the half-life of a 2nd order reaction depends inversely on the initial concentration:

t_1/2 = 1 / (2 · k_eff · [B]₀)

The theoretical maximum yield of product C as $t \rightarrow \infty$ is limited by the initial moles of reactant B: n_C,max = (V_B · [B]₀) / 2.