The answer depends on the mechanism. For example:
The mechanism here is just a proton colliding with a water molecule. So can predict intuitively that the reaction rate is proportional to the concentrations of each component, because higher concentrations increase the chance of a collision. Experiments confirm this model.
Not everyone collision results in a reaction. It needs to collide fast enough and at the right angle, for example the proton needs to collide with the oxygen atom in water. These effects are represented by a rate constant k.
Above is a gas phase example, but many reactions in solvents behave similarly, such as protonation of water by HCL:
The reason the collision has to be fast enough is to overcome the activation energy - the energy of the transition state, which is when the new bond is partially formed and the old one is partially broken:
Transition states are just energy maxima, they cannot be isolated because any change in the structure pushes it towards a lower energy state. It would be like balancing a marble on top of a football, without friction.
The rate constant is also the part which varies with temperature.
The rate constant can be related to temperature and the activation energy of the reaction using the Eyring equation:
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