In solution, hypochlorite ion is known to decompose with a second-order rate law. If [ClO-]0 = 0.0570 M and k = 2.06x10-4 M-1·min-1, calculate the half-life for this reaction 2ClO- 2Cl- + O2.
To calculate the half-life of a second-order reaction, you can use the integrated rate law for a second-order reaction.
The integrated rate law for a second-order reaction is:
1/[A]t = kt + 1/[A]0
Where [A]t and [A]0 are the concentrations of the reactant at time 't' and at the beginning of the reaction, respectively.
In this case, the reactant is the hypochlorite ion (ClO-) and its initial concentration ([ClO-]0) is given as 0.0570 M. The rate constant (k) is given as 2.06x10^-4 M^-1·min^-1.
Let's rearrange the integrated rate law to solve for time (t) when the concentration of the reactant ([A]t) is half of its initial concentration ([A]0):
1/[A]t = kt + 1/[A]0
Plugging in the values:
1/(0.5*[ClO-]0) = k*t + 1/[ClO-]0
1/(0.5*0.0570) = 2.06x10^-4 * t + 1/0.0570
1/0.0285 = 2.06x10^-4 * t + 1/0.0570
Solving this equation will give you the value of time (t), which represents the half-life of the reaction.