Introduction To Chemistry
Introduction To Chemistry
5th Edition
ISBN: 9781259911149
Author: BAUER, Richard C., Birk, James P., Marks, Pamela
Publisher: Mcgraw-hill Education,
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Chapter 9, Problem 130QP
Interpretation Introduction

Interpretation:

The volume occupied by argon gas in the new system is to be determined.

Concept Introduction:

Ideal gas law is followed by ideal gases. It states that the pressure P and the volume V of gas are directly proportional to the number of moles n present in the gas and temperature T of the gas.

PV=nRT … (1)

Dalton’s law of partial pressure states that the total pressure of the mixture of gases is equal to the sum of partial pressures of the gases present in the mixture.

PTotal=P1+P2+P3+..........+Pn

Expert Solution & Answer
Check Mark

Answer to Problem 130QP

Solution:

The volume occupied by argon gas in new system is 2.88 L .

Explanation of Solution

Given Information: The volume of argon gas collected over water is 3 L at 27.0°C and 765 torr . The vapor pressure of water at 15°C is 13 torr .

A sample of 3 L argon gas is bubbled through and collected over water at 27.0°C and 765 torr . Thus, the number of moles present in the argon gas can be calculated using ideal gas law.

Convert temperature units from Celsius to Kelvin as,

TK=T°C+273.15

For 27.0°C ,

T1=27.0°C+273.15=300.15 K

Covert pressure units from torr to atm as,

1 atm=760 torr1 torr=1760 atm

For 765 torr ,

765 torr=1 atm760 torr×765 torr=1.01 atm

Substitute V as 3 L , T as 300.15 K , P as 1.01 atm and R as 0.08206 L atm mol1K1 in equation (1).

1.01 atm×3 L=n×0.08206 L atm mol1K1×300.15 Kn=1.01 atm×3 L0.08206 L atm mol1K1×300.15 K=0.123 mol

Thus, 0.123 mol of argon gas is collected over water. The temperature and pressure of the new system are 15°C and 778 torr . The total pressure of the system and the partial pressure of water is known. So, the partial pressure of argon gas in the new system can be determined using Dalton’s law.

PTotal=PArgon+PWater …(2)

Substitute PWater as 13 torr and PTotal as 778 torr in equation (2).

778 torr=PArgon+13 torrPArgon=778 torr13 torr=765 torr

The new pressure of argon gas in new system is 765 torr . Thus, the volume occupied by argon gas in new system is determined using ideal gas law.

Covert pressure units from torr to atm as,

1 atm=760 torr1 torr=1760 atm

For 765 torr ,

765 torr=1 atm760 torr×765 torr=1.01 atm

Convert temperature units from Celsius to Kelvin as,

TK=T°C+273.15

For 15.0°C ,

T1=15.0°C+273.15=298.15 K

Substitute P as 1.01 atm , T as 298.15 K , n as 0.123 mol and R as 0.08206 L atm mol1K1 in equation (1).

1.01 atm×V=0.123 mol×0.08206 L atm mol1K1×298.15 KV=0.123 mol×0.08206 L atm mol1K1×298.15 K1.01 atm=2.88 L

Conclusion

The volume occupied by argon gas in the new system is 2.88 L .

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Chapter 9 Solutions

Introduction To Chemistry

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