Fraction converted in a half-hour run

Question

Problem 1: A 10-minute experimental run shows that 75% of liquid reactant is converted to product by a half-order rate. What would be the fraction converted in a half-hour run?

Problem 2: After 8 minutes in a batch reactor reactant (CA0 = 1 mol/L) is 80% converted; after 18 minutes, conversion is 90%. Find a rate equation to represent this reaction.

Problem 3: Aqueous A at a concentration of CA0 = 1 mol/L is introduced into a batch reactor where it reacts away to form product R according to stoichiometry

A -> R

The concentration of A in the reactor is monitored at various times, as shown below:

Time, min      C_A, mol/m³
0                      1000
100                   500
200                   333
300                   250
400                   200

(a) For C_A0 = 500 mol/m3 find the conversion of reactant after 5 hours in the batch reactor.

(b) Find the rate expression for the reaction.