Answer:
It will take 188.06 hours for the concentration of A to decrease 10.0% of its original concentration.
Explanation:
A → B
Initial concentration of the reactant = x
Final concentration of reactant = 10% of x = 0.1 x
Time taken by the sample, t = ?
Formula used :
[tex]A=A_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}[/tex]
where,
[tex]A_o[/tex] = initial concentration of reactant
A = concentration of reactant left after the time, (t)
[tex]t_{\frac{1}{2}}[/tex] = half life of the first order conversion = 56.6 hour
[tex]\lambda[/tex] = rate constant
[tex]A=A_o\times e^{-(\frac{0.693}{t_{1/2}})\times t}[/tex]
Now put all the given values in this formula, we get
[tex]0.1x=x\times e^{-(\frac{0.693}{56.6 hour})\times t}[/tex]
t = 188.06 hour
It will take 188.06 hours for the concentration of A to decrease 10.0% of its original concentration.
