The reactor is the heart of most chemical plants, and its size, temperature and type decide most of what comes after. This lesson recaps what the course uses from Physical chemistry and Material and energy balances, so you can start here.
The rate of a reaction, r, is how fast a substance is used or made per unit volume, in mol/(L·min) or mol/(m³·s). A rate law ties it to concentration: for a first-order reaction A → products, −r_A = k × C_A, where C_A is A's concentration and k the rate constant (units: per time). The minus sign says A is being used up.
The rate constant rises with temperature by the Arrhenius equation, k = A·e^(−Ea/RT), where Ea is the activation energy and R = 8.314 J/(mol·K). Comparing two temperatures: k₂/k₁ = e^[(Ea/R)(1/T₁ − 1/T₂)].
Conversion, X, is the fraction of a reactant that has reacted: C_A = C_A0 × (1 − X) for a liquid, where C_A0 is the starting concentration. X = 0.9 means 90% is gone and 10% left.
From balances: in − out + generation − consumption = accumulation. A reactor's design equation is just that balance for the reactant, with the rate law plugged in. ln is the natural log (calculator key ln), and ln(1/(1 − X)) turns up a lot: for X = 0.9 it's ln 10 = 2.303.
C_A0 = 2.0 mol/L and conversion is 75%. What is C_A, in mol/L?
| First order | −r_A = kC_A |
|---|---|
| Conversion | C_A = C_A0(1 − X) |
| Arrhenius | k = A·e^(−Ea/RT) |
| ln(1/(1−X)) | X 0.5 → 0.693, X 0.9 → 2.303 |