A minuscule pinhole develops in the wall of a tank, and every molecule of the gas inside that strikes the hole escapes from the pressure vessel. Calculate the number of nitrogen molecules that effuse per second through a round hole of 0.01 mm diameter if the gas is at 25 °C and one bar.

Given,Diameter of round hole = 0.01 mmTemperature of the gas = = (273 + 25) K = 298 KPressure of…

Answered: A miniscule pinhole develops in the…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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A minuscule pinhole develops in the wall of a tank, and every molecule of the gas inside that strikes the hole escapes from the pressure vessel. Calculate the number of nitrogen molecules that effuse per second through a round hole of 0.01 mm diameter if the gas is at 25 °C and one bar.

Expert Solution

Step 1: Variables given

Given,

Diameter of round hole = 0.01 mm

Temperature of the gas = $25 to the power of ring operator C$ = (273 + 25) K = 298 K

Pressure of the gas = 1 bar = 10⁵ pa

The process in which a gas escapes from a small hole is called effusion. Number of nitrogen molecules that effuse per second is the rate effusion. The kinetic theory of gases can be used to obtain the effusion formula as follows.

Effusion flux = $P divided by left parenthesis 2 pi m K T right parenthesis to the power of 1 divided by 2 end exponent$ = $N subscript A P divided by left parenthesis 2 pi M R T right parenthesis to the power of 1 divided by 2 end exponent$

Rate of Effusion = Effusion flux $cross times$ area of the hole (A_hole)

where N_A = Avogadro's constant = 6.022 $cross times 10 to the power of 23$

k = Boltzmann's constant

T = Temperature in K

P = Pressure in Pascals

R = gas constant in J/(K mol) = 8.314 J/(Kmol)

M = Molar mass in kg of the material that is effusing

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