Chemistry

The key insight is that reaction rate depends both on the rate constant and the concentration term raised to the order power: $\text{rate} = k[A]^n$. Since all three reactions have identical $k$ values, the one with the highest concentration dependence will dominate—but only when concentrations are high enough. At very low concentrations, the first-order reaction (linear in $[A]$) will actually be fastest because higher-order reactions are suppressed by smaller concentration terms. This reveals an important principle: rate constant alone doesn't determine speed; the interplay between $k$ and $[A]^n$ shifts which reaction is fastest depending on the concentration regime.

The key insight is that reaction rate depends both on the rate constant and the concentration term raised to the order power: $\text{rate} = k[A]^n$. Since all three reactions have identical $k$ values, the one with the highest concentration dependence will dominate—but only when concentrations are high enough. At very low concentrations, the first-order reaction (linear in $[A]$) will actually be fastest because higher-order reactions are suppressed by smaller concentration terms. This reveals an important principle: rate constant alone doesn't determine speed; the interplay between $k$ and $[A]^n$ shifts which reaction is fastest depending on the concentration regime.