## Half-life

$\frac{d[R]}{dt}=-k; [R]=-kt + [R]_{0}; t_{\frac{1}{2}}=\frac{[R]_{0}}{2k}$

Nicholas Le 4H
Posts: 74
Joined: Fri Sep 28, 2018 12:24 am

### Half-life

What exactly is a half-life? I do not understand the concept behind this.

julia_lok_2K
Posts: 56
Joined: Fri Sep 28, 2018 12:25 am

### Re: Half-life

A half life is the time it takes for a substance to fall/decay/be consumed to half its original concentration. Half lives do not depend on the concentration, i.e. the half life of a substance remains the same at any stage in the reaction. We use the t1/2=0.693/k equation to relate half life to the rate constant, so if a problem asks for or requires the rate constant but gives the half life, then you would use this equation. Also, from this equation, we can see that half-life and k are inversely proportional. This makes sense conceptually because the larger k is, the faster the reaction proceeds, so the less time it would take for a substance to fall to half its initial value.

Hope this helps!

Lumbini Chandrasekera 1B
Posts: 63
Joined: Fri Sep 28, 2018 12:18 am

### Re: Half-life

A half life is the time it takes for half of a substance to decompose or change. For radioactive elements, I believe, it is the time it takes for half of that element (let's say half of 4 g which is = 2 g) to disappear. In chemical reactions, it would be the time it takes half of the concentration of something to disappear.

Douglas Nguyen 2J
Posts: 71
Joined: Fri Sep 28, 2018 12:15 am

### Re: Half-life

Half-life is the amount of time it takes for a species to be reduced to half of its concentration!

Alexandra Albers 1D
Posts: 61
Joined: Fri Sep 28, 2018 12:18 am

### Re: Half-life

Even though half-life only determines the time required for a substance to decay to half of its original amount, in a half-life problem we may be asked to determine the time for a substance to decay to any amount. We should be able to manipulate the equation for half-life in order to find these values though.

Anmol_cheema_2F
Posts: 60
Joined: Fri Sep 28, 2018 12:26 am

### Re: Half-life

The half life of a reactant is simply the time needed for its concentration to fall to 1/2 its initial value.

Hannah Yates 1K
Posts: 59
Joined: Fri Sep 28, 2018 12:27 am

### Re: Half-life

It’s just the amount of time it takes for the reactant to become half its original concentration. What’s interesting with half life is that this time never changes no matter the amount of concentration you start with.