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

Dear student

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

Lets say the initial concentration is A0 .
Now the percentage decomposition in first minute is 1% i.e, now the concentration of A that is left is 
A0 - (A0/100) = 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 ‚ÄčIn 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. 


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