Question

sodium-24 has a half life of 15 hours. Suppose you had a sample containing 0.010 moles of Na-24. How many hours would be required to reduce your sample to 6.25x10^-4 moles

Answer 1

Answer : The time required would be, 60.0 hours

Explanation :

Half-life = 15 hr

First we have to calculate the rate constant, we use the formula :

`k=(0.693)/(t_(1/2))`

`k=\frac{0.693}{15\text{ hr}}`

`k=0.0462\text{ hr}^(-1)`

Now we have to calculate the time passed.

Expression for rate law for first order kinetics is given by:

`t=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant =
`0.0462\text{ hr}^(-1)`

t = time passed by the sample = ?

a = initial amount of the reactant = 0.010 mol

a - x = amount left after decay process = 6.25 × 10⁻⁴ mol

Now put all the given values in above equation, we get

`t=(2.303)/(0.0462)\log(0.010)/(6.25* 10^(-4))`

`t=60.0\text{ hr}`

Therefore, the time required would be, 60.0 hours