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The average distance that a molecule travels before colliding with another molecule is called the mean free path and is given by 1 where d is the diameter of the molecule and N, is the number of molecules per unit volume. The number of collisions that a molecule makes with other molecules per unit time, or collision frequency f, is given by f = avg (a) Determine the mean free path (in m) of hydrogen molecules in a tank that has a volume of 12.5 L, a gauge pressure of 110 atm, and a temperature of 20.0°C. The average diameter of hydrogen molecules is 0.740 x 10-10 m. 1.49E-8 m (b) Determine the average time interval (in s) between molecular collisions for a molecule of hydrogen gas. 0.52

The average distance that a molecule travels before colliding with another molecule is called the mean free path and is given by 1 where d is the diameter of the molecule and N, is the number of molecules per unit volume. The number of collisions that a molecule makes with other molecules per unit time, or collision frequency f, is given by f = avg (a) Determine the mean free path (in m) of hydrogen molecules in a tank that has a volume of 12.5 L, a gauge pressure of 110 atm, and a temperature of 20.0°C. The average diameter of hydrogen molecules is 0.740 x 10-10 m. 1.49E-8 m (b) Determine the average time interval (in s) between molecular collisions for a molecule of hydrogen gas. 0.52

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The average distance that a molecule travels before colliding with another molecule is called the mean free path and is given by: where d is the diameter of the molecule and N, is the number of molecules per unit volume. The number of collisions that a molecule makes with other molecules per unit time, or collision frequency f, is given by f = avg (a) Determine the mean free path (in m) of hydrogen molecules in a tank that has a volume of 12.5 L, a gauge pressure of 110 atm, and a temperature of 20.0°C. The average diameter of hydrogen molecules is 0.740 x 10¬10 m. 1.49E-8 m (b) Determine the average time interval (in s) between molecular collisions for a molecule of hydrogen gas. 0.52 How is the time of interest related to the collision frequency? Check the text for an expression for the average speed. Remember to express the molecular mass in terms of kilograms and that the temperature must be in kelvins. s
Transcribed Image Text:The average distance that a molecule travels before colliding with another molecule is called the mean free path and is given by: where d is the diameter of the molecule and N, is the number of molecules per unit volume. The number of collisions that a molecule makes with other molecules per unit time, or collision frequency f, is given by f = avg (a) Determine the mean free path (in m) of hydrogen molecules in a tank that has a volume of 12.5 L, a gauge pressure of 110 atm, and a temperature of 20.0°C. The average diameter of hydrogen molecules is 0.740 x 10¬10 m. 1.49E-8 m (b) Determine the average time interval (in s) between molecular collisions for a molecule of hydrogen gas. 0.52 How is the time of interest related to the collision frequency? Check the text for an expression for the average speed. Remember to express the molecular mass in terms of kilograms and that the temperature must be in kelvins. s
Expert Solution
Step 1

Part (a)

Given:

  • The volume of tank is V=12.5 L.
  • The gauge pressure of tank is Pg=110 atm.
  • The temperature of tank is T=20.0∘C.
  • The diameter of molecules is d=0.740×10-10 m.

The temperature of tank in Kelvin is calculated as,

T=20.0∘C+273 K=293 K

The formula to calculate the total pressure of tank is,

P=Pa+Pg

Here, P is the total pressure, Pa is the atmospheric pressure and Pg is the gauge pressure.

Substitute the known values in the formula to calculate the total pressure of tank.

P=1 atm+110 atm=111 atm1.013×105 Pa1 atm=112.4×105 Pa

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