(i) Concentration:
According to the law of mass action, the rate of a chemical reaction is directly proportional to the concentration of reactants. Higher concentration \(\Rightarrow\) more molecules per unit volume \(\Rightarrow\) greater frequency of effective collisions \(\Rightarrow\) higher reaction rate. For example, doubling the concentration of reactant in a first-order reaction doubles the rate.
(ii) Temperature:
Raising temperature increases the kinetic energy of molecules. This leads to:
- More frequent collisions, and
- A higher fraction of molecules possessing energy greater than the activation energy.
As per the Arrhenius equation, \(k = Ae^{-E_a/RT}\), the rate constant \(k\) increases exponentially with temperature. Roughly, a \(10^\circ C\) rise in temperature nearly doubles the rate of many reactions.
(iii) Catalyst:
A catalyst provides an alternate reaction pathway with lower activation energy (\(E_a\)). This does not affect the equilibrium position but significantly increases the rate at which equilibrium is achieved. Both homogeneous and heterogeneous catalysts enhance the velocity by lowering the energy barrier for effective collisions.
\[
\boxed{\text{Thus, concentration, temperature, and catalyst all increase the velocity of a reaction.}}
\]