A drop of solution (volume `0.05 mL`) contains `3 xx 10^(-6) "mole" H^(o+)` ions. If the rate constant of disappearance of `H^(o+)` ions is `1 xx 10^(7) mol L^(-1) s^(-1)`, how long would it take for `H^(o+)` ions in the drop of disappear?

Options

A. `6 xx 10^(-8) sec`
B. `6 xx 10^(-7) sec`
C. `6 xx 10^(-9) sec`
D. `6 xx 10^(-10) sec`

Answer

C

Explanation

time Total for drop to disappears
`(a_(0) - a_(t)) = k_(t) a_(t) = 0`
`(3.0 xx 10^(-6))/((0.05 xx 10^(-3)) xx 1.0 xx 10^(-7)) = t_(100%)`
`rArr t_(100%) = 6 xx 10^(-9) sec`
Alternative method
Units rate constant `= mol L^(-1) sec^(-1) rArr` Zero order reaction.
`[A_(0)] - [A] = kT` `[A_(0)] = (3 xx 10^(-6) xx 100)/(0.05 xx 10^(-3)) = (3)/(50)`
`(3)/(50) - 0 = kT`
`rArr t = (3)/(50) xx (10^(-7))/(1)`
`= 6 xx 10^(-9) sec`