half-life for second order runs

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

Payton Kammerer 2B
Posts: 49
Joined: Tue May 01, 2018 3:00 am

half-life for second order runs

A half life is the time it takes for the reactant concentration to decrease by half, but how does that work when the stoichiometric coefficients of a chemical equation are not all 1? Does each reactant get a separate half-life, or is the concentration of all the reactants to be summed for an overall reactant concentration value?

Helen Struble 2F
Posts: 97
Joined: Sat Aug 24, 2019 12:17 am

Re: half-life for second order runs

Half-lives are rarely ever used for second order reactions anyway since they are dependent on the initial concentration. Half-lives are more useful for first order rate laws, because they allow you to deduce certain information about the reaction without knowing the initial concentration at all.

Miriam Villarreal 1J
Posts: 105
Joined: Sat Aug 17, 2019 12:16 am

Re: half-life for second order runs

Half-life of second order reactions decrease at a much faster rate. Length of half life increases as you go down while the concentration of substrate constantly decreases, unlike zero and first order reaction.