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From Wikipedia,

Collision theory is a theory ... that qualitatively explains how chemical reactions occur and why reaction rates differ for different reactions. The collision theory states that when suitable particles of the reactant hit each other, only a certain percentage of the collisions cause any noticeable or significant chemical change; these successful changes are called successful collisions. The successful collisions must have enough energy, also known as activation energy, at the moment of impact to break the preexisting bonds and form all new bonds.

From Britannnica,

Law of mass action, law stating that the rate of any chemical reaction is proportional to the product of the masses of the reacting substances, with each mass raised to a power equal to the coefficient that occurs in the chemical equation.

How can both explain and imply each other?

My theory: Due to more availability of reacting species (due to more amount), rate of reaction of increases. But it does not explain the reason of exponentiation of stoichiometric coefficients.

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For exponentiation, we can say that it is actually repeated multiplication. Comparing two cases:

  • $$\ce{A + B -> AB}$$ Here, the rate expression is $r=K[\ce{A}][\ce{B}]$. This is because one molecule of $\ce{A}$ and one molecule of $\ce{B}$ is needed for the product to form.
  • $$\ce{2A + B -> A2B}$$ First, write it in this way: $$\ce{A + A + B -> A2B}$$ Now, rate expression is $r=K\ce{[A][A][B]}$. That's it - $r=K[\ce{A}]^2[\ce{B}]$

An intuitive starting point for me to understand why concentrations are multiplied is probably to connect it with multiplication theorem in probability (for independent events).

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