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Match the gas sample on the left with a description on the right.
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0.115 moles of Xe in a 4.87 L container at a temperature of 446K
0.599 moles of Xe in a 5.78 L container at a temperature of 306K
0.444 moles of Xe in a 2.39 L container at a temperature of 408K
0.556 moles of Xe in a 2.11 L container at a temperature of 446K
has the highest average molecular speed
has the lowest average molecular speed
has an average molecular speed between the highest and the lowest

Container 2 has the lowest average molecular speed

Container 4 has the highest average molecular speed

Explanation:

Step 1: Data given

Atomic mass of Xe = 131.29 g/mol

Container 1: Number of moles Xe = 0.115 moles; volume = 4.87 L; temperature= 446K

Container 2: Number of moles Xe = 0.599 moles; Volume = 5.78 L; temperature= 306K

Container 3: Number of moles Xe = 0.444 moles; Volume = 2.39L; Temperature = 408K

Container 4: Number of moles Xe = 0.556 moles; Volume=2.11L; Temperature =446K

Step 2: Calculate average molecular speed

Average molecular speed V = √(8RT/πM)

→With R = he gas constant expressed in units of J/mol-K

→with T = the temperature in Kelvin

→with M = the molar mass of the gas

Average molecular speed depends on T and M

Since it's all Xenon, M is the samefor the 4 containers

Container 1:

V1 = √(8*8.314*446K/π*131.29)

V1 = 8.48

has an average molecular speed between the highest and the lowest

V2= √(8*8.314*306K/π*131.29)

V2= 7.03

has the lowest average molecular speed

V3 = √(8*8.314*408K/π*131.29)

V3 = 8.11

has an average molecular speed between the highest and the lowest

V4 = √(8*8.314*446K/π*131.29)

V4 = 8.48

Since the volume is smaller than in container 1 the average molecular speed will be a higher

has the highest average molecular speed