Explanation Explanation To derive: the equation for average kinetic energy and total kinetic energy. From the 4 th postulate of kinetic molecular theory, the average kinetic energy of gas is directly proportional to the Kelvin temperature of the gas. By applying the principle of physics to the assumption of kinetic molecular theory the ideal gas law and expression for pressure can be derived. Expression for pressure, P = 2/3 [ n ( KE ) avg V ] or PV n = 2/3 ( KE ) avg The relation between temperature and average kinetic energy can be written as, since ( KE ) avg µ T PV n = 2/3 ( KE ) avg µ T or PV n µ T 2/3 ( KE ) avg = R T = PV n ( KE ) avg = 3/2 ×R T for 1 mole of gas ... ( 1 ) where, R = proportionality constant or universal constant ( 8 .314J/K mol ) K E t o t a l = ( n a r g o n + n m e t h a n e ) × 3 / 2 × R T From the 4 th postulate of kinetic molecular theory, the average kinetic energy of gas is directly proportional to the Kelvin temperature of the gas. By applying this postulate, the equation for average kinetic energy can be derived. To determine the average kinetic energy per molecule, molar average kinetic energy should be divided by Avogadro’s number . Total kinetic energy can be determined by multiplying the sum of number of moles of each gas to the equation (1). To find: the number of moles of argon Number of moles = mass in gram gram molecular mass From the given data, Mass of argon = 228 g Molecular mass = 39 .95 g/mol n Ar = 228 g 39 .95 g/mol = 5 .71 mol Number of moles of argon is determined by dividing the given mass to the molecular mass. To find: the number of moles of methane. Total kinetic energy can be determined as, K E t o t a l = ( n a r g o n + n m e t h a n e ) × 3 / 2 × R T Since the mole fraction of metahne ( χ CH 4 ) in the mixture is 0

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Question

Chapter 8, Problem 102E

Interpretation Introduction

Interpretation: For the given data, Total kinetic energy of gaseous mixture of methane and argon should be determined.

Concept introduction:

Kinetic molecular theory explains the properties of ideal gas. From the postulates of kinetic molecular theory it is clear that kinetic energy of gas particle is directly proportional to the Kelvin temperature of the gas.

Average kinetic energy of gas can be determined as, KEavg= (3/2)RT

Total kinetic energy can be determined as, KEtotal=(nargon+nmethane) ×3/2 ×R T

Expert Solution & Answer

Chapter 8 Solutions

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Solution Summary: The author explains that kinetic energy of gas particle is directly proportional to the Kelvin temperature of the gas.

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Chapter 8 Solutions