Answer:
5:22 am
Explanation:
The gas X decays following a first-order reaction.
The half-life ([tex]t_{1/2}[/tex]) is 25 min. We can find the rate constant (k) using the following expression.
[tex]k = \frac{ln2}{t_{1/2}} =\frac{ln2}{25min} = 0.028 min^{-1}[/tex]
We can find the concentration of X at a certain time ([tex][X][/tex]) using the following expression.
[tex][X] = [X]_0 \times e^{-k \times t}[/tex]
where,
[tex][X]_0[/tex]: initial concentration of X
t: time elapsed
[tex]\frac{[X]}{[X]_0}= e^{-k \times t}\\\frac{1/10[X]_0}{[X]_0}= e^{-0.028min^{-1} \times t}\\t=82min[/tex]
The earliest time Professor Utonium can come back to do experiments in the lab is:
4:00 + 82 = 5:22 am
