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The half life is the amount of time for half the reaction to occur. If the reaction rate is higher, it means the reaction happens faster, so then the amount of time to get to half of the final state would be shorter.
For a first-order reaction, the half-life is equal to ln2/kr which means that when kr, the rate constant, increases, the half-life will decrease since kr is in the denominator and they are inversely proportional. The same proportion is true for the zeroth and second half-lives as they have kr in the denominator meaning that they are inversely proportional and an increase in one leads to a decrease in the other.
In all of the half life equations for 0th, 1st, and 2nd order rate laws, the rate constant is in the denominator, and so when you increase the rate constant the half life becomes smaller. Alternatively you can think of it as the rate constant increasing leads to a faster reaction meaning that the decay of the reactant will occur quicker and half life will be shorter.
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