Question

five samples of krypton gas are described in the table below. rank the samples in order of increasing average kinetic energy of the atoms in them. that is, select \1\ next to the sample in which the krypton atoms have the lowest average kinetic energy. select \2\ next to the sample in which the krypton atoms have the next lowest average kinetic energy, and so on.

sample
1.7 mol	1.9 atm	-34. °c	select
1.4 mol	1.5 atm	-26. °c	select
2.0 mol	2.4 atm	-24. °c	select
2.9 mol	2.9 atm	-44. °c	select
1.5 mol	1.7 atm	-32. °c	select

Explanation:

Step1: Recall KE-temperature relation

Average kinetic energy (KE) of gas atoms depends only on absolute temperature ($T$ in Kelvin), not amount or pressure. Formula: $\overline{KE} = \frac{3}{2}kT$ (k = Boltzmann constant).

Step2: Convert °C to Kelvin

$T(K) = T(^\circ C) + 273.15$

• 1.7 mol sample: $-34 + 273.15 = 239.15\ K$
• 1.4 mol sample: $-26 + 273.15 = 247.15\ K$
• 2.0 mol sample: $-24 + 273.15 = 249.15\ K$
• 2.9 mol sample: $-44 + 273.15 = 229.15\ K$
• 1.5 mol sample: $-32 + 273.15 = 241.15\ K$

Step3: Rank by T (lowest to highest)

Order of T: $229.15 < 239.15 < 241.15 < 247.15 < 249.15$

Step4: Assign ranks to samples

• 2.9 mol (-44°C): 1
• 1.7 mol (-34°C): 2
• 1.5 mol (-32°C): 3
• 1.4 mol (-26°C): 4
• 2.0 mol (-24°C): 5

Answer:

2.9 mol, 2.9 atm, -44°C: 1
1.7 mol, 1.9 atm, -34°C: 2
1.5 mol, 1.7 atm, -32°C: 3
1.4 mol, 1.5 atm, -26°C: 4
2.0 mol, 2.4 atm, -24°C: 5