You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds 0.9000.900 L. The pressure of the gas inside the balloon equals air pressure (1.001.00 atm). If the air inside the balloon is at a constant 22.022.0°C and behaves as an ideal gas, what mass of air can you blow into one of the balloons before it bursts?

Ch 18: Thermal Properties of Matter

Young & Freedman Calc - University Physics 15th Edition

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Young & Freedman Calc 15th Edition

Ch 18: Thermal Properties of Matter

Problem 6a

Chapter 18, Problem 6a

You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds $0.900$ L. The pressure of the gas inside the balloon equals air pressure ( $1.00$ atm). If the air inside the balloon is at a constant $22.0$ °C and behaves as an ideal gas, what mass of air can you blow into one of the balloons before it bursts?

Verified step by step guidance

First, understand that the problem involves the ideal gas law, which is given by the equation:

P V = n R T

, where

P

is the pressure,

V

is the volume,

n

is the number of moles,

R

is the ideal gas constant, and

T

is the temperature in Kelvin.

Convert the given temperature from Celsius to Kelvin using the formula:

T

_k=T_c+273.15. For 22.0°C, this becomes

22.0 + 273.15

Substitute the known values into the ideal gas law equation. Use

P = 1.00 atm

V = 0.900 L

, and the converted temperature in Kelvin. The ideal gas constant

R

0.0821 L atm mol

^-1 K^-1.

Solve for the number of moles

n

using the rearranged ideal gas law:

n = P V R T

Finally, convert the number of moles to mass. Use the molar mass of air, which is approximately

28.97 g mol

^-1. Multiply the number of moles by the molar mass to find the mass of air that can be blown into the balloon before it bursts.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in physics that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law helps determine the amount of gas that can be added to a balloon before it bursts.

Conversion of Temperature to Kelvin

In gas law calculations, temperature must be expressed in Kelvin. To convert from Celsius to Kelvin, add 273.15 to the Celsius temperature. For this problem, the given temperature is 22.0°C, which converts to 295.15 K. This conversion is crucial for accurately applying the Ideal Gas Law.

Molar Mass of Air

The molar mass of air is an average value based on the composition of gases in the atmosphere, primarily nitrogen and oxygen. It is approximately 28.97 g/mol. Knowing the molar mass allows us to convert between the number of moles and the mass of air, which is necessary to find out how much air can be added to the balloon before it bursts.

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