# if one percent of the reactant decomposes in first minute in a first order reaction calculate how much reactant would remain undecomposed after one hour

We can use the equation for the first order kinetics as:

Lets say the initial concentration is A

_{0}.

Now the percentage decomposition in first minute is 1% i.e, now the concentration of A that is left is

A

_{0}- (A

_{0}/100) = 0.99Ao.

so the equation becomes,

0.99 Ao = Ao e

^{-k1min}

So 0.99 = e

^{-k1min}

ln 0.99 = -k *1 min

so k = - ln 0.99

So In 1 hour or 60 minutes thus the

new concentration of the reactant will be,

A = Ao(e

^{-(-ln 0.99)*60 min})

So A = 0.5471 Ao

so after the given time, 54.71% of the initial reactant will be remaining.

Regards

**
**