For a first-order reaction, rate = k[A], where rate is directly proportional to reactant concentration.
Run 1: 100 mL of 10 M solution
Concentration = 10 M
Rate: r1=k×10
Run 2: 200 mL of 10 M solution
Concentration remains 10 M (increasing volume doesn't change concentration)
Rate: r2=k×10
Therefore r1=r2
Run 3: 100 mL of 10 M solution + 100 mL of H₂O
Total moles of A = 10 M × 0.1 L = 1 mol
Total volume = 0.2 L
New concentration = 1 mol / 0.2 L = 5 M
Rate: r3=k×5
Therefore r3<r1=r2