The Arrhenius equation and activation energy (HL)

Answer

**k = A·e^{−E_{a}/RT}** — it gives the rate constant in terms of the frequency factor A, the activation energy E_{a}, the gas constant R and the absolute temperature T.

Answer

The **frequency of collisions** and whether they occur with the **correct orientation** (the steric factor). A has the **same units as k**.

Answer

The **activation energy** — the minimum collision energy needed to react. It sits in the **exponent**, so it has a large effect on k.

Answer

R = the **gas constant** = **8.31 J K⁻¹ mol⁻¹**; T = the **absolute temperature in kelvin** (°C + 273).

Answer

Because E_{a}/RT shrinks as T rises and the term is **exponential** — a small T increase makes a large k increase (often k roughly doubles per 10 K).

Answer

**ln k = ln A − (E_{a}/R)(1/T)** — the equation of a straight line for ln k against 1/T.

Answer

**y-axis = ln k**, **x-axis = 1/T** (T in kelvin).

Answer

**−E_{a}/R** — a negative value (because E_{a} > 0).

Answer

**ln A** — the value of ln k when 1/T = 0; so A = e^{intercept}.

Answer

**E_{a} = −gradient × R**, then **÷ 1000** to convert J mol⁻¹ → kJ mol⁻¹.

Answer

**ln(k₂/k₁) = −(E_{a}/R)(1/T₂ − 1/T₁)** — used to find E_{a} from rate constants at two temperatures.

Answer

**(1)** Forgetting the minus sign — E_{a} = −gradient × R. **(2)** Forgetting to ÷ 1000, since R is in **J** K⁻¹ mol⁻¹, so E_{a} comes out in J mol⁻¹.