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Chemical Reaction Rates and Equilibrium

CSCA Chemical Reaction Rates and Equilibrium study guide organized around the publicly available CSCA syllabus. Practice Chemistry questions on aicsca.com.

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Chemical Reaction Rates and Equilibrium

Core Concepts and Learning Objectives

This section studies chemical reactions from a dynamic perspective. It involves not only the change of substances (**Reaction Rate**) but also the limit of the reaction (**Chemical Equilibrium**).

**Learning Objectives:**

1. **Calculation**: Master the calculation of reaction rates and the relationship between rates of different substances.

2. **Mechanism**: Understand how concentration, temperature, pressure, and catalysts affect rates (Collision Theory).

3. **Equilibrium Criteria**: Deeply understand the "Dynamic, Equal, Constant, Changeable" characteristics and the Equilibrium Constant $K$.

4. **Dynamic Analysis**: Apply Le Chatelier's Principle to determine the direction of equilibrium shift.

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I. Chemical Reaction Rate

#### 1. Definition and Expression

Measures how fast a reaction proceeds. Usually expressed as the decrease in reactant concentration or increase in product concentration per unit time.

* **Formula**: $v = \frac{|\Delta c|}{\Delta t}$

* **Unit**: $mol\cdot L^{-1}\cdot s^{-1}$ or $mol\cdot L^{-1}\cdot min^{-1}$

* **Key Rule**: For reaction $aA + bB \rightleftharpoons cC + dD$, the ratio of rates equals the ratio of stoichiometric coefficients:

$$ \frac{v(A)}{a} = \frac{v(B)}{b} = \frac{v(C)}{c} = \frac{v(D)}{d} $$

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#### 2. Factors Affecting Rate

* **Intrinsic**: Nature of reactants (decisive factor).

* **Extrinsic** (Conditions):

1. **Concentration**: Higher concentration $\rightarrow$ More active molecules per unit volume $\rightarrow$ More frequent effective collisions $\rightarrow$ **Faster Rate**.

2. **Pressure** (Gases): Higher pressure $\equiv$ Smaller volume $\equiv$ Higher concentration $\rightarrow$ **Faster Rate**.

3. **Temperature**: Higher temperature $\rightarrow$ Percentage of activated molecules increases significantly $\rightarrow$ **Rate increases significantly**.

4. **Catalyst**: Lowers Activation Energy ($E_a$) $\rightarrow$ More molecules become activated $\rightarrow$ **Increases both forward and reverse rates equally**.

5. **Surface Area** (Solids): Crushing solids $\rightarrow$ Larger area $\rightarrow$ **Faster Rate**.

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II. Chemical Equilibrium

#### 1. Establishment and Characteristics

Under given conditions, when **Forward Rate = Reverse Rate**, the concentrations of all substances stop changing. This is Chemical Equilibrium.

* **Characteristics**:

* **Reversible**: Applies to reversible reactions.

* **Dynamic**: $v_{fwd} = v_{rev} \neq 0$. Reaction hasn't stopped.

* **Equal**: Rates are equal.

* **Constant**: Concentrations remain constant.

* **Shift**: Equilibrium shifts if conditions change.

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#### 2. Equilibrium Constant ($K$)

For $aA(g) + bB(g) \rightleftharpoons cC(g) + dD(g)$, $K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$.

* **Meaning**: Larger $K$ means the reaction proceeds further to the right.

* **Note**:

* $K$ depends **ONLY on Temperature**.

* Solids and pure liquids are **omitted** from the $K$ expression.

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III. Le Chatelier's Principle

**Principle**: If a condition (concentration, pressure, temperature) acting on a system at equilibrium is changed, the system will shift to **counteract** the change.

| Change | Shift Direction | Reason |

| :--- | :--- | :--- |

| **Increase** Reactant Conc. | **Forward** (Right) | Consume added reactant |

| **Decrease** Product Conc. | **Forward** (Right) | Replace lost product |

| **Increase** Pressure (Volume $\downarrow$) | To side with **fewer** gas moles | Reduce pressure buildup |

| **Increase** Temperature | To **Endothermic** direction | Absorb excess heat |

| Add **Catalyst** | **No Shift** | Changes $v_{fwd}$ and $v_{rev}$ equally |

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IV. Typical Examples

**Ex 1: Rate Conversion**

Reaction $N_2 + 3H_2 \rightleftharpoons 2NH_3$. If $v(NH_3) = 0.5$, what is $v(H_2)$?

* **Sol**: Ratio is $3:2$. $v(H_2) = \frac{3}{2} v(NH_3) = 0.75$.

**Ex 2: Pressure Effect**

$2NO_2(g) \rightleftharpoons N_2O_4(g)$ (Red-brown $\leftrightarrow$ Colorless). Compress the syringe to half volume.

* **Sol**:

1. **Instant**: Volume halves, concentration doubles $\rightarrow$ Color **darkens instantly**.

2. **Shift**: Pressure up, shifts to fewer moles (Right/Colorless).

3. **Final**: Color fades slightly from the peak but remains **darker** than the original state.

**Ex 3: Inert Gas (Trap)**

Add Helium (He) at constant temperature:

* **Case A (Constant Volume)**: Total P up, but partial pressures unchanged $\rightarrow$ **No Shift**.

* **Case B (Constant Pressure)**: Volume expands $\rightarrow$ Partial pressures drop $\rightarrow$ Shifts to side with **more** gas moles.

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V. Common Pitfalls

1. **Start vs. Limit**: Catalysts help you reach equilibrium faster, but do not change the yield ($K$).

2. **Pressure Trap**: If gas moles are equal on both sides (e.g., $H_2 + I_2 \rightleftharpoons 2HI$), changing pressure changes Rate but **NOT Equilibrium**.

3. **Calculation Method**: Always use the **"ICE Table" (Initial, Change, Equilibrium)** method for calculations to avoid errors.