# Reaction Kinetics

Chemistry I · Atoms, Bonds and Reaction Rates · https://tryals.app/learn/chemistry-i/reaction-kinetics

## Rate, Order and Mechanism

Thermodynamics says whether a reaction *can* happen; kinetics says how fast. For $aA \to$ products the rate law is

$$\text{rate} = k[A]^m$$

where the **order** $m$ is found by experiment, never read off the balanced equation. The **method of initial rates** compares runs: if doubling $[A]$ doubles the rate the reaction is first order in A; if it quadruples it, second order; if nothing changes, zero order.

Integrating gives the forms used to test data by straight-line plots:

| Order | Integrated law | Linear plot | Half-life |
|---|---|---|---|
| Zero | $[A] = [A]_0 - kt$ | $[A]$ against $t$ | $[A]_0/2k$ |
| First | $\ln[A] = \ln[A]_0 - kt$ | $\ln[A]$ against $t$ | $\ln 2 / k$ |
| Second | $1/[A] = 1/[A]_0 + kt$ | $1/[A]$ against $t$ | $1/k[A]_0$ |

The first-order half-life is the striking one: it is **independent of starting concentration**, which is why radioactive decay and many drug clearances have a single quoted half-life.

Most reactions proceed through several **elementary steps**, and the slowest, the rate-determining step, controls the overall rate. Only for an elementary step may you read the order straight from its stoichiometry.

Temperature dependence follows **Arrhenius**:

$$k = A e^{-E_a/RT}$$

Raising $T$ increases the fraction of collisions carrying at least the activation energy $E_a$, which is why a modest rise can double a rate. A **catalyst** provides a different pathway with a lower $E_a$ and is regenerated unchanged. Crucially, it speeds the forward and reverse reactions equally, so it changes how *fast* equilibrium arrives but never *where* it lies.

> **Common pitfall:** reading reaction order off the balanced equation. Order is experimental. The overall equation reflects only the net stoichiometry, while the rate law reflects the mechanism, and for $\mathrm{2NO_2 + F_2}$, the reaction is first order in $\mathrm{F_2}$ despite its coefficient of 1 and first order in $\mathrm{NO_2}$ despite its coefficient of 2.

## Practice questions

8 of this lesson's 12 practice questions, with answers. The full set is in the app.

### 1. Doubling the concentration of reactant A leaves the reaction rate unchanged. Which order with respect to A best explains this?

A. Half order
B. Second order
C. First order
D. Zero order

**Answer:** D. Zero order

**Why:** Rate $\propto [A]^m$, so doubling $[A]$ multiplies the rate by $2^m$. An unchanged rate means $2^m = 1$, giving $m = 0$, zero order, typical of surface-saturated catalytic reactions.

Page: https://tryals.app/practice/chemistry-i/reaction-kinetics/doubling-the-concentration-of-reactant-a-leaves-the-reaction-rate

### 2. The order of a reaction can always be read directly from the coefficients of its balanced equation.

**Answer:** False

**Why:** False, the balanced equation gives net stoichiometry, not mechanism. Order must be measured, and matches the coefficients only for a genuinely elementary step.

Page: https://tryals.app/practice/chemistry-i/reaction-kinetics/the-order-of-a-reaction-can-always-be-read-directly-from-the

### 3. When $[A]$ is doubled, the rate of a reaction increases by a factor of 4. What is the order with respect to A?

**Answer:** 2

**Why:** The rate multiplies by $2^m$, so $2^m = 4$ gives $m = 2$, second order in A. Its half-life would then depend on the starting concentration, unlike a first-order reaction.

Page: https://tryals.app/practice/chemistry-i/reaction-kinetics/when-a-is-doubled-the-rate-of-a-reaction-increases-by-a-factor-of

### 4. Sort each quantity by whether adding a catalyst changes it.

**Answer:**

- Changed by a catalyst: Activation energy of the pathway, Rate constant of the forward reaction, Time taken to reach equilibrium
- Unchanged by a catalyst: Position of the equilibrium, Enthalpy change of the reaction, Equilibrium constant

**Why:** A catalyst lowers the barrier, so both rate constants rise and equilibrium arrives sooner. But the reactants and products are unchanged, so $\Delta H$ is fixed, and because both directions speed up equally their ratio, the equilibrium constant, cannot shift.

Page: https://tryals.app/practice/chemistry-i/reaction-kinetics/sort-each-quantity-by-whether-adding-a-catalyst-changes-it

### 5. Which statements about the first-order half-life are correct?

A. Each successive half-life takes the same time
B. It doubles whenever the starting concentration doubles
C. It equals ln 2 divided by the rate constant
D. It is independent of the starting concentration

**Answer:** A. Each successive half-life takes the same time; C. It equals ln 2 divided by the rate constant; D. It is independent of the starting concentration

**Why:** For first order, $t_{1/2} = \ln 2/k$ contains no concentration term, so it is constant throughout the reaction. Dependence on starting concentration is a feature of zero- and second-order kinetics.

Page: https://tryals.app/practice/chemistry-i/reaction-kinetics/which-statements-about-the-first-order-half-life-are-correct

### 6. Thermodynamics governs whether a transformation is spontaneous, whereas kinetics governs its pathway and rate. What follows from this distinction when evaluating a catalyst's role in a system?

A. It alters the overall reaction pathway to produce a thermodynamically richer yield
B. It accelerates the approach to equilibrium without shifting the final position
C. It lowers the activation barrier for the forward reaction whilst leaving the reverse unchanged
D. It transforms an energetically unfavourable transformation into a feasible spontaneous pathway

**Answer:** B. It accelerates the approach to equilibrium without shifting the final position

**Why:** Thermodynamic quantities depend solely on initial and final states, meaning a catalyst cannot alter equilibrium composition or drive non-spontaneous reactions. By lowering the activation barrier equally in both directions, it accelerates the exchange rate without perturbing the balance of species.

Page: https://tryals.app/practice/chemistry-i/reaction-kinetics/thermodynamics-governs-whether-a-transformation-is-spontaneous

### 7. A first-order reaction has a half-life of 25 s. What percentage of the original reactant remains after 75 s?

**Answer:** 12.5 (within ±0.6)

**Why:** 75 s is $75/25 = 3$ half-lives, so the fraction remaining is $(1/2)^3 = 1/8 = 12.5$ %. Note the reactant is never entirely consumed in a first-order process.

Page: https://tryals.app/practice/chemistry-i/reaction-kinetics/a-first-order-reaction-has-a-half-life-of-25-s-what-percentage-of

### 8. In an elementary reaction step, the order with respect to each reactant does equal its stoichiometric coefficient.

**Answer:** True

**Why:** True, an elementary step *is* the collision event, so its rate is proportional to the concentrations of exactly the species colliding, raised to how many of each take part. This is the one case where reading order off the equation is valid.

Page: https://tryals.app/practice/chemistry-i/reaction-kinetics/in-an-elementary-reaction-step-the-order-with-respect-to-each