Loose Leaf For Explorations:  Introduction To Astronomy
Loose Leaf For Explorations: Introduction To Astronomy
9th Edition
ISBN: 9781260432145
Author: Thomas T Arny, Stephen E Schneider Professor
Publisher: McGraw-Hill Education
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Chapter 6, Problem 7P
To determine

The mass of oxygen gas in the atmosphere.

Expert Solution & Answer
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Answer to Problem 7P

The mass of oxygen gas in the atmosphere is 1.2×1018kg_.

Explanation of Solution

Given that the total mass of Earth’s atmosphere is 5.1×1018kg, the percentage abundance of N2, O2, and Ar in the atmosphere is 78%, 21%, and 1% respectively.

Let X be the number of oxygen molecules in the atmosphere. The atomic mass of N2 is 14×1.66×1027kg, the atomic mass of O2 is 16×1.66×1027kg, and the atomic mass of Ar is 18×1.66×1027kg.

Write the expression for finding the molecular mass of N2, O2, and Ar can be computed as,

  MN2=2×14×1.66×1027kgMO2=2×16×1.66×1027kgMAr=1×18×1.66×1027kg}        (I)

Since the percentage abundance of N2, O2, and Ar in the atmosphere is 78%, 21%, and 1% respectively, for each molecule of O2,there will be 78/21 N2 molecules, and 1/21 Ar atoms.

Thus, the total mass of the atmosphere can e expressed as,

  Mtotal=(7821X)MN2+(121X)MAr+(X)MO2=X[7821MN2+121MAr+MO2]        (II)

Solve equation (II) for X.

  X=Mtotal[7821MN2+121MAr+MO2]        (III)

The total mass of O2 in the atmosphere can be then computed as,

  Mtotal O2=XMO2        (IV)

Use equation (III) in (IV).

  Mtotal O2=MtotalMO2[7821MN2+121MAr+MO2]        (V)

Conclusion:

Substitute 5.1×1018kg for Mtotal, 2×14×1.66×1027kg for MN2, 2×16×1.66×1027kg for MO2, and 1×18×1.66×1027kg for MAr in equation (V) to find Mtotal O2.

  Mtotal O2=(5.1×1018kg)(2×16×1.66×1027kg)[7821(2×14×1.66×1027kg)+121(1×18×1.66×1027kg)+(2×16×1.66×1027kg)]=1.19×1018kg1.2×1018kg

Therefore, the mass of oxygen gas in the atmosphere is 1.2×1018kg_.

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Loose Leaf For Explorations: Introduction To Astronomy

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