Which sample is the average kinetic energy of the particles the greatest

The answer to your question is below

Explanation:

1)

Data

Temperature 1 = 498°C

Pressure 1 = 13.8 atm

Volume 1 = ?

Temperature 2 = 29°C

Pressure 2 = 2 atm

Volume 2 = 18 L

Process

1.- Convert temperature to °K

Temperature 1 = 498 + 273 = 771 °K

Temperature 2 = 29 + 273 = 302 °K

2.- Use the combine law of gas

              P1V1/T1 = P2V2/T2

Solve for V1

             V1 = T1P2V2 / P1T2

Substitution

             V1 = (771)(2)(18) / (13.8)(302)

Simplification

             V1 = 27756 / 4167.6

Result

             V1 = 6.66 L

2)

Use Boyle's law to solve this problem

             P1V1 = P2V2

Data

P1 = 2 atm

V1 = 2.5 L

P2 = ?

V2 = 4 L

- Solve for P2

             P2 = P1V1/V2

- Substitution

             P2 = (2)(2.5) / 4

- Simplification

             P2 = 5 / 4

- Result

              P2 = 1.25 atm