Project ForgeChemical Reaction Engineering
Reaction Kinetics
GATE 2014
Hard
A homogeneous reaction (R→P) occurs in a batch reactor. The conversion of the reactant R is 67% after 10 minutes and 80% after 20 minutes. The rate equation for this reaction is
- A−rR = k
- −rR = k·CR²
- C−rR = k·CR³
- D−rR = k·CR^0.5
Explanation
Testing second order: the integrated law gives X/(1−X)=C0·k·t, which should be exactly proportional to t. At t=10: X/(1−X)=0.67/0.33=2.03. At t=20: 0.80/0.20=4.00. The ratio 4.00/2.03≈1.97≈2, matching the ratio of times (20/10=2) — confirming a direct proportionality to t, i.e. second order kinetics.
Source: GATE CH 2014 (2014)
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