Chemistry: An Atoms-Focused Approach
Chemistry: An Atoms-Focused Approach
14th Edition
ISBN: 9780393912340
Author: Thomas R. Gilbert, Rein V. Kirss, Natalie Foster
Publisher: W. W. Norton & Company
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Chapter 10, Problem 10.82QA
Interpretation Introduction

To find:

The number of balloons that will float in air.

Expert Solution & Answer
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Answer to Problem 10.82QA

Solution:

Only one balloon filled with He gas will float in the air.

Explanation of Solution

1) Concept:

We are given the density of the air, the four gases, the temperature, and the pressure. The ideal gas equation is

PV=nRT

n=mM

where n=  number of moles of a gas, m=  mass in grams of a gas, M=  molar mass of the gas. If we plug the value of n in the ideal gas equation, the equation will be modified into

PV=mM RT

Rearranging the equation for  m, we get

m=PVMRT

So, using this equation, we need to find the mass of each of the gas in the balloons. Adding the mass of empty balloons to the mass of the gas, we will get the mass of the balloon filled with a gas. Using the density formula, we calculate the density of each balloon filled with gas. Comparing the density of each balloon filled with a gas with the density of air will give number of balloons that can float in air. If the density of the balloon is equal or less than the given density of air, the balloon will float. If the density of the balloon filled with a gas is greater than the density of air, the balloon will not float. We note that among the given gases, Helium (He) has the lowest molar mass. So, the mass of the balloon filled with the gas He is expected to have a density less than the density of air.

2) Formula:

i. d=M×PRT

ii.

m=PMVRT

iii.

d=mV

3) Given:

i) Mass of empty balloon = 10.0 g

ii) Volume of a balloon = 20.0 L

iii) Four gases are: He, Ne, CO2and CO

iv) Density of air = 1.17 g/L

v) Temperature = 25 =25+273=295 K

4) Calculations:

Using the above modified formula for mass in grams, we find mass of each gas in the balloon, and then find the mass of balloon as

i) Calculations for Helium balloon:

m=PVMRT

m=1.00 atm ×20.0 L×4.003 g/mol0.08206 L·atmmol·K×298K=3.273 g

Mass of the balloon filled with Helium gas can be calculated as

Total mass of balloon=Mass of empty balloon+Mass of balloon filled with the gas

Total mass of balloon=10g+3.273g=13.273g

Calculating density of each of the given gases as

d=mV

d=13.273g20.0 L=0.66365 g/L

Thus, density of He balloon is less than the given density of air. So, helium balloon will float in the air.

ii) Calculations for Neon balloon:

m=PVMRT

m=1.00 atm ×20.0 L×20.18 g/mol0.08206 L·atmmol·K×298K=16.504 g

Mass of the balloon filled with Neon gas can be calculated as

Total mass of balloon=Mass of empty balloon+Mass of balloon filled with the gas

Total mass of balloon=10g+16.504g=26.504g

Calculating density of each of the given gases as

d=mV

d=26.504g20.0 L=1.3252 g/L

Thus, density of Ne balloon is greater than the given density of air. So, Ne balloon will not float in air.

iii) Calculations for CO2 balloon:

m=PVMRT

m=1.00 atm ×20.0 L×44.01 g/mol0.08206 L·atmmol·K×298K=35.9942 g

Mass of the balloon filled with carbon dioxide gas can be calculated as

Total mass of balloon=Mass of empty balloon+Mass of balloon filled with the gas

Total mass of balloon=10g+35.9942g=45.9942g

Calculating density of each of the given gases as

d=mV

d=45.9942g20.0 L=2.299 g/L

Thus, density of CO2 balloon is greater than the given density of air. So, CO2 balloon will not float in air.

iv) Calculations for CO balloon:

m=PVMRT

m=1.00 atm ×20.0 L×28.01 g/mol0.08206 L·atmmol·K×298K=22.9084 g

Mass of the balloon filled with carbon monoxide gas can be calculated as

Total mass of balloon=Mass of empty balloon+Mass of balloon filled with the gas

Total mass of balloon=10g+22.9084=32.9084g

Calculating density of each of the given gases as

d=mV

d=32.9084g20.0 L=1.6045 g/L

Thus, density of CO  balloon is greater than the given density of air. So, CO  balloon will not float in air.

From above calculated densities of gases filled with different gases, the balloon filled with He  gas can only float in air as its density is smaller than the density of the air at the mentioned conditions of the temperature and the pressure.

Conclusion:

From the modified ideal gas equation, we calculated the densities of balloons filled with each gas and compared them to the given density of air. Balloons with the density equal to or less than that of air will float in air.

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Chapter 10 Solutions

Chemistry: An Atoms-Focused Approach

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