Reaction Rates - Chemistry

1. Fundamental Concepts

Definition: Reaction rate is the speed at which a chemical reaction occurs. It measures how quickly reactants are consumed or products are formed.

Non-constancy: Reaction rates are not constant. They are usually fastest at the start of the reaction and slow down over time as reactants are used up.

2. Key Concepts

A. Expressing Rate

Units: Typically Molarity per second ($M/s$ or $mol \cdot L^{-1} \cdot s^{-1}$).

General Formula:

$$ \text{Rate} = \frac{\Delta \text{Concentration}}{\Delta \text{Time}} = \frac{\Delta [X]}{\Delta t} $$

Sign Convention:

Reactants: Rate is expressed as negative ($-\frac{\Delta [R]}{\Delta t}$) because concentration decreases.

Products: Rate is expressed as positive ($\frac{\Delta [P]}{\Delta t}$) because concentration increases.

B. Stoichiometric Relationships

The rate of change for different substances is related by their mole ratios (coefficients) in the balanced equation.

For a general reaction: $aA(g) + bB(g) \rightarrow cC(g) + dD(g)$

The relationship is:

$$ -\frac{1}{a}\frac{\Delta [A]}{\Delta t} = -\frac{1}{b}\frac{\Delta [B]}{\Delta t} = \frac{1}{c}\frac{\Delta [C]}{\Delta t} = \frac{1}{d}\frac{\Delta [D]}{\Delta t} $$

C. Graphical Representation

Concentration vs. Time Plot:

The slope of the line at any given point represents the rate of the reaction at that moment.

Reactants show a negative slope (decreasing).

Products show a positive slope (increasing).

3. Examples

Easy

Question: In the reaction $4NH_3(g) + 5O_2(g) \rightarrow 4NO(g) + 6H_2O(g)$, which substance has the fastest rate of change?

Answer: $H_2O(g)$

Explanation: The rate of change is directly proportional to the coefficient in the balanced equation. Since $H_2O$ has the largest coefficient (6), its concentration changes the most over time.

Medium

Question: For the decomposition reaction $2N_2O_5(g) \rightarrow 4NO_2(g) + O_2(g)$, the concentration of $N_2O_5(g)$ decreases from $1.0 \, M$ to $0.5 \, M$ in $100$ seconds. What is the average rate of disappearance of $N_2O_5(g)$?

Answer: $0.005 \, M/s$

Calculation:

$$ \text{Rate} = -\frac{\Delta [N_2O_5]}{\Delta t} = -\frac{(0.5 - 1.0)}{100} = -\frac{(-0.5)}{100} = 0.005 \, M/s $$

Hard

Question: Consider the combustion reaction $C_3H_8(g) + 5O_2(g) \rightarrow 3CO_2(g) + 4H_2O(g)$. If the rate of formation of $CO_2(g)$ is $0.30 \, M/s$, what is the rate of consumption of $O_2(g)$?

Answer: $0.50 \, M/s$

Calculation:

1. Set up the ratio using coefficients:

$$ \frac{1}{5} \text{Rate}(O_2) = \frac{1}{3} \text{Rate}(CO_2) $$

2. Rearrange to solve for $O_2$:

$$ \text{Rate}(O_2) = \frac{5}{3} \times \text{Rate}(CO_2) $$

3. Substitute the value:

$$ \text{Rate}(O_2) = \frac{5}{3} \times 0.30 = 0.50 \, M/s $$

4. Problem-Solving Techniques

Check the Coefficients:

Always start with a balanced chemical equation.

Remember that the rate divided by the coefficient is the same for all substances in the reaction.

Interpret the Slope:

On a graph of $[Concentration]$ vs. $Time$:

Steepness = Speed: A steeper slope means a faster reaction rate.

Flat Line = Stop: When the curve becomes horizontal, the slope is zero, meaning the reaction has completed.

Use Dimensional Analysis:

If you need to find a concentration, the units should be $M$.

If you need to find a rate, the units must include "per time" ($/s$, $/min$).

Conversion: $\Delta [X] = \text{Rate} \times \Delta t$