Arate is equal to 0.0200 m/s. if [a] = 0.100 m and rate = k[a][b]2, what is the new rate if the concentration of [a] is increased to 0.200 m?

The new rate is 0.0400 mol·L⁻¹s⁻¹.

r = k[A][B]²

The reaction is first order in [A].

If you double [A], you double the rate.

The new rate is 2 × 0.0200 mol·L⁻¹s⁻¹ = 0.0400 mol·L⁻¹s⁻¹ .

the old alchemists made significant contributions to science even though there starting premises were off a bit. their conclusions after failure would steer them into better directions for investigation. science is no more than close observation and the initial mistakes result in rethinking and retrying experiments.