## missylulu one year ago hi. a first-order reaction has a half life of 26.4 seconds. how long will it take for the concentration of the reactant in the reaction to fall to 1/8 of its initial value? please help me omg

1. miley28

i'll give u an easy formula for this.. time taken for conc. of reactant to fall is, n*half life=initial conc/$2^{n}$

2. miley28

since here it is given 1/8 of its initial value so accordin to the formula, 3*26.4=initial conc/$2^{3}$ thus time taken is=3*26.4=79.2secs

3. miley28

but remember this formula is only applicable for 1st order reactions... or elase u may apply the general rate constant formulas.

4. aaronq

first order reaction so use: $t _{1/2}=\frac{ \ln2 }{ k }$ find k then, use: $A=A _{0}e ^{-kt}$ assume Ao= initial = 1 then A = 1/8 solve for t, time, which will be in seconds

5. missylulu

what formula is A = Ao e^-kt ??

6. aaronq

general equation for exponential decay or growth

7. missylulu

oh that's right gahh sorry LOL