Explanation The change in pressure due to height is given below as, p = p o exp ( − ( M g h R T ) ) (1) Where, Ø p is the partial pressure of the gas. Ø p o is the standard pressure of the gas. Ø ρ is the density. Ø g is the gravitational constant having the value of 9.8 m s − 2 . Ø R is the gas constant. Ø h is the height. Ø M is the molar mass of the gas. The equation for partial pressure of nitrogen can be written as, p N 2 = p o,N 2 exp ( − ( M N 2 g h R T ) ) (2) The equation for partial pressure of oxygen can be written as, p O 2 = p o,O 2 exp ( − ( M O 2 g h R T ) ) (3) The expression for height can be obtained by dividing the equation (2) and (3) as, p N 2 p O 2 = p o,N 2 exp ( − ( M N 2 g h R T ) ) p o,O 2 exp ( − ( M O 2 g h R T ) ) p N 2 p O 2 × p o,O 2 p o,N 2 = exp ( − ( M N 2 g h R T ) − ( − ( M O 2 g h R T ) ) ) ln ( p N 2 p O 2 × p o,O 2 p o,N 2 ) = g h ( M O 2 − M N 2 ) R T h = R T g ( M O 2 − M N 2 ) × ln ( p N 2 p O 2 × p o,O 2 p o,N 2 ) The molar mass of nitrogen and oxygen are 28.02 g mol − 1 and 32.00 g mol − 1 respectively. The pressure of a gas is equal to its composition at constant temperature. Substitute the corresponding values in the above equation as follows. h = R T g ( M O 2 − M N 2 ) × ln ( p N 2 p O 2 × p o,O 2 p o,N 2 ) = ( 8

11th Edition

ISBN: 9780198769866

Author: ATKINS, P. W. (peter William), De Paula, Julio, Keeler, JAMES

Publisher: Oxford University Press

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Question

Chapter 1, Problem 1A.14P

Interpretation Introduction

Interpretation:

The height above the surface of earth at which the atmosphere becomes 90 % nitrogen and 10 % oxygen by mass has to be calculated. The pressure of the atmosphere at that height has to be calculated.

Concept introduction:

The perfect gas equation is given for the gases which follow a specific rule under certain conditions. This is represented by the formula given below as,

pV=nRT

The pressure due to height difference is given by the formula as,

p=poexp(−(MghRT))

Expert Solution & Answer

Chapter 1 Solutions

Atkins' Physical Chemistry

Ch. 1 - Prob. 1A.1ST Ch. 1 - Prob. 1A.2ST Ch. 1 - Prob. 1B.1ST Ch. 1 - Prob. 1C.1ST Ch. 1 - Prob. 1A.1DQ Ch. 1 - Prob. 1A.1AE Ch. 1 - Prob. 1A.1BE Ch. 1 - Prob. 1A.2AE Ch. 1 - Prob. 1A.2BE Ch. 1 - Prob. 1A.3AE

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