   # At 0°C a 1.0-L flask contains 5.0 × 10 −2 mole of N 2 , 1.5 × 10 2 mg O 2 , and 5.0 × 10 21 molecules of NH 3 . What is the partial pressure of each gas, and what is the total pressure in the flask? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 8, Problem 88E
Textbook Problem
152 views

## At 0°C a 1.0-L flask contains 5.0 × 10−2 mole of N2, 1.5 × 102 mg O2, and 5.0 × 1021 molecules of NH3. What is the partial pressure of each gas, and what is the total pressure in the flask?

Interpretation Introduction

Interpretation: The total pressure of given flask, the partial pressures of each gas in the flask is needed to be determined.

Concept introduction:

• Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.

Partial pressure of a gas in terms of its mole fraction and total pressure is,

PA=χA×PTOTAL

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

Equation for mole fraction of a molecule in a mixture of three molecules (A, B and C) is,

moleculefractionofA,(χA=Numbersof moles ofmolecule A(nA)Total number of moles(nA+nB+nC

• Number of moles of a substance,

From its given mass is,

Number of moles=GivenmassMolecularmass

From its given number of molecules is,

Number of moles=number of molecules6.022×1023molecules

• Total pressure of a flask containing mixture of gases is the sum of individual partial pressures of constituted gases.

Pressure of the flask, according to ideal gas equation,

Pressure=Numberofmoles×R×TemperatureVolume

### Explanation of Solution

Explanation

• To find: the number of moles of O2 and NH3 from their given mass and numbers of molecules respectively.

The number of moles of O2 is 4.7×10-3mol .

The number of moles of NH3 is 8.3×10-3mol .

• The given mass for O2 is 1.5×102mg=1.5×102mg×1g1000mg=0.15g

Number of moles of a substance from its given mass is,

Number of moles=GivenmassMolecularmass

Therefore, the number of moles of O2 in the flask is,

Number of moles O2=0.15g32g/mol=4.7×10-3mol

• The given number of molecules for NH3 is 5×1021molecules .

Number of moles of a substance from its given number of molecules is,

Number of moles=number of molecules6.022×1023molecules

Therefore, the number of moles of NH3 in the flask is,

Number of moles NH3=5×1021molecules×1mol6.022×1023molecules=8.3×10-3mol

• To find: the total pressure of the given flask.

The total pressure of the given flask is 1.4atm .

The number of moles of N2 is given as 5×10-2mol .

The number of moles of O2 is calculated as 4.7×10-3mol .

The number of moles of NH3 is calculated as 8.3×10-3mol .

Therefore,

The total number of moles of gases presented in the flask is,

5×10-2mol+4.7×10-3mol+8.3×10-3mol=6.3×10-2mol

The volume of flask is given as 1L .

The temperature of flask is given as 0oC=273K .

The total pressure of the flask is determined by using ideal gas equation for finding pressure.

Pressure of the flask, according to ideal gas equation,

Total pressure=Total numberofmoles×R×TemperatureVolume

Therefore,

The total pressure of the flak is,

Total pressure=6.3×10-2mol×0.08206Latm/Kmol×273K1L =1

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