Question

The boiling point of Krypton $(Kr)$ and Radon $(Rn)$ are $ - {152^\circ }C$ and $ - {62^\circ }C$ respectively. Calculate the approximate boiling point of xenon.

Answer 1

Hint: As we know that noble gases are the inert elements of periodic table and possess a low melting point and boiling point and the elements also follow the law of triad as we know that it states that the properties of the middle element in a group of three elements is between those of the other two adjacent elements.

Complete step-by-step solution:As we know that Dobereiner’s law of triad states that the properties of the middle element in a group of three lies between those of the other two members of the group or we can say that the characteristics of the middle element is an arithmetic mean of the other two elements.
We also know that Krypton, Xenon and Radon form a triad in the noble gases members of the periodic table. So we can say that Xenon possesses some similar characteristics or properties in between Krypton and Radon. Similarly, we can assume that the boiling point of Xenon must lie between the boiling points of Krypton and Radon.
So using the above information we can calculate the average of the boiling points to identify the boiling point of Xenon. So, we will get:
$B.{P_{Xenon}} = \dfrac{{B.{P_{Krypton}} + B.{P_{Radon}}}}{2}$
$\Rightarrow B.{P_{Xenon}} = \dfrac{{( - {{152}^\circ }C) + ( - {{62}^\circ }C)}}{2}$
$\Rightarrow B.{P_{Xenon}} = \dfrac{{ - {{214}^\circ }C}}{2}$
$\therefore B.{P_{Xenon}} = - {107^\circ }C$

Therefore, from the above calculation, the correct answer is $B.{P_{Xenon}} = - {107^\circ }C$.

Note:Remember that noble gases are chemically unreactive and among the inert elements Xenon and Radon are one of the rarest elements of the group. But the ionisation enthalpy of xenon is somewhat identical to the oxygen and thus xenon is known to form a red colour compound of the platinum fluoride and thus a number of xenon compounds are known with electronegative fluoride and oxygen. Krypton has only one known compound which is $Kr{F_2}$.