# Reaction rates and collision reasoning

Physics I · Chemistry · https://tryals.app/learn/physics-i/reaction-rates-and-collision-reasoning

## Reaction Kinetics & Rates

**Chemical kinetics** studies **how fast** reactions proceed, rather than just thermodynamic favourability.

**Rate law**: $v = k\,[A]^{m}\,[B]^{n}$

| Symbol | Meaning |
| --- | --- |
| $v$ | Reaction rate |
| $k$ | Rate constant |
| $m, n$ | **Reaction orders** (found experimentally, **never** from balanced equations) |

**Collision theory**: Reactions require molecules to **collide** with sufficient kinetic energy $\ge E_a$ (activation energy) and correct **orientation**.

## Arrhenius & Catalysts

**Arrhenius equation**: $k = A\,e^{-E_a / RT}$

- $A$: frequency factor
- $E_a$: activation energy
- $R$: $8.314\text{ J mol}^{-1}\text{K}^{-1}$

Linear form: $\ln k = \ln A - \frac{E_a}{R}\cdot\frac{1}{T}$. Plotting $\ln k$ vs $1/T$ gives slope $-E_a/R$.

**Catalysts** lower $E_a$ without being consumed.

**Key insight**: Doubling temperature dramatically increases rates due to exponential dependence.

**Common pitfall**: A catalyst speeds the journey but never moves the destination. It lowers forward and reverse barriers equally, changing rate, not equilibrium.

## Practice questions

6 of this lesson's 13 practice questions, with answers. The full set is in the app.

### 1. Raising the temperature speeds a reaction mainly by making molecules collide more often.

**Answer:** False

**Why:** False. Collision frequency rises only with $\sqrt{T}$, a few percent for a 10 K rise, while the *fraction* of molecules exceeding the activation energy rises exponentially through the Boltzmann factor. That exponential term is what roughly doubles many rates for every 10 K, not the extra collisions.

Page: https://tryals.app/practice/physics-i/reaction-rates-and-collision-reasoning/raising-the-temperature-speeds-a-reaction-mainly-by-making-molecules

### 2. Complete the statement with the correct term.

**Answer:** For a first-order reaction A → products, the rate law is rate = k·[A]ⁿ. The exponent n equals **1**.

**Why:** First-order means rate ∝ [A]¹. The exponent (reaction order) is 1, and the half-life $t_{1}$/₂ = $\ln(2)$/k is independent of concentration.

Page: https://tryals.app/practice/physics-i/reaction-rates-and-collision-reasoning/complete-the-statement-with-the-correct-term

### 3. Raising temperature speeds a reaction far more than the increase in collision frequency alone predicts. Why does the speed-up outrun the rise in collision frequency?

A. From the decrease in activation energy at higher temperature
B. From the increase in the number of molecules present
C. From the greater volume the gas occupies when heated
D. From the fraction of collisions above the activation barrier

**Answer:** D. From the fraction of collisions above the activation barrier

**Why:** The exponential dominates completely. This is why a 10 °C rise can double a rate while collision frequency changes by under 2%.

Page: https://tryals.app/practice/physics-i/reaction-rates-and-collision-reasoning/raising-temperature-speeds-a-reaction-far-more-than-the-increase-in

### 4. A catalyst can speed a reaction a **million-fold** and is recovered unchanged at the end. Why does that not violate anything?

A. It makes the products more stable, so the reaction is driven further
B. It lowers the activation barrier by offering another route
C. It supplies the extra energy the reaction needs, which it later reabsorbs
D. It increases the number of collisions by raising the effective temperature

**Answer:** B. It lowers the activation barrier by offering another route

**Why:** Only the barrier moves; the endpoints do not. That is exactly why a catalyst cannot shift an equilibrium, it speeds the forward and reverse directions by the same factor and changes when equilibrium is reached, never where. Supplying or absorbing energy would make it a reactant, and it would not be recovered.

Page: https://tryals.app/practice/physics-i/reaction-rates-and-collision-reasoning/a-catalyst-can-speed-a-reaction-a-million-fold-and-is-recovered

### 5. Which statements about the Arrhenius equation $k = A\cdot e^{-E_{a}/RT}$ are correct?

A. A catalyst increases k by lowering $E_{a}$
B. A higher $E_{a}$ gives a faster reaction at any temperature
C. k increases as temperature T increases
D. k is independent of reactant concentration

**Answer:** A. A catalyst increases k by lowering $E_{a}$; C. k increases as temperature T increases; D. k is independent of reactant concentration

**Why:** A higher $E_{a}$ slows the reaction (fewer molecules have enough energy), not speeds it up.

Page: https://tryals.app/practice/physics-i/reaction-rates-and-collision-reasoning/which-statements-about-the-arrhenius-equation-k-a-e-ea-rt-are

### 6. Complete the statements about reaction kinetics.

**Answer:** The **rate law** expresses reaction rate as a function of concentration: rate $= k[A]^m$. For $m = 2$, the reaction is **second** order in A. The **activation energy** $E_{a}$ is the minimum kinetic energy required for a collision to produce a reaction.

**Why:** Reaction order is determined experimentally, not from stoichiometric coefficients in the balanced equation.

Page: https://tryals.app/practice/physics-i/reaction-rates-and-collision-reasoning/complete-the-statements-about-reaction-kinetics