## Rate Constant and Shorter Half Life

Michelle N - 2C
Posts: 117
Joined: Wed Sep 18, 2019 12:19 am

### Rate Constant and Shorter Half Life

Can someone explain to me about the relationship about the higher the rate constant, the shorter its half-life? Thank you!

MingdaH 3B
Posts: 133
Joined: Thu Jul 11, 2019 12:17 am

### Re: Rate Constant and Shorter Half Life

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.

805394719
Posts: 104
Joined: Wed Sep 11, 2019 12:16 am

### Re: Rate Constant and Shorter Half Life

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.

805307623
Posts: 99
Joined: Fri Aug 09, 2019 12:17 am

### Re: Rate Constant and Shorter Half Life

The half-life of a first-order reaction is inversely proportional to the rate constant k. A fast reaction has a larger k and shorter half-life. A slow reaction has a smaller k and longer half-life.

Pablo 1K
Posts: 118
Joined: Sat Feb 02, 2019 12:15 am

### Re: Rate Constant and Shorter Half Life

If the rate content is high it means the reaction occurs quicker the higher the constant. In turn, the half life is reached at a quicker rate.

Ryan Yee 1J
Posts: 101
Joined: Sat Aug 17, 2019 12:16 am

### Re: Rate Constant and Shorter Half Life

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.