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 :

$k=\frac{0.693}{t_{1/2}}$

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

$k=0.0462\text{ hr}^{-1}$

Now we have to calculate the time passed.

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

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

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

$t=\frac{2.303}{0.0462}\log\frac{0.010}{6.25\times 10^{-4}}$

$t=60.0\text{ hr}$

Therefore, the time required would be, 60.0 hours