Calculating the Initial Number of Moles

Oct 13, 2025 by thesweetdesigns.com 133 views

Introduction

Air is a mixture of gases that surrounds our planet, and its properties can be affected by changes in temperature and pressure. In this article, we will explore the behavior of air at a specific temperature and pressure, and then calculate its final temperature and mass after being compressed to a different volume and pressure.

Initial Conditions

The initial conditions of the air are given as follows:

Temperature: 17 C
Pressure: 940 torr (absolute)
Volume: 2.46 m^3
Gas constant (R): 287 J/kg K

We can use the ideal gas law to relate these properties:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

Converting Units

Before we can use the ideal gas law, we need to convert the units of the given values to a consistent set of units. We will use the following conversions:

17 C = 290 K (temperature in Kelvin)
940 torr = 124.3 kPa (pressure in Pascals)
2.46 m^3 = 2460000 cm^3 (volume in cubic centimeters)

Calculating the Initial Number of Moles

We can now use the ideal gas law to calculate the initial number of moles of air:

n = PV / RT

Substituting the given values, we get:

n = (124.3 kPa * 2460000 cm^3) / (287 J/kg K * 290 K)

n ≈ 0.016 kg

Calculating the Initial Mass

The initial mass of the air can be calculated by multiplying the number of moles by the molar mass of air. The molar mass of air is approximately 28.97 g/mol.

m = n * M

where m is the mass and M is the molar mass.

m ≈ 0.016 kg * 28.97 g/mol ≈ 0.465 g

Final Conditions

The air is compressed to a final volume of 1000000 cm^3 and a pressure of 103 PSI. We need to convert the final pressure to Pascals:

103 PSI ≈ 707.9 kPa

Calculating the Final Temperature

We can use the ideal gas law again to calculate the final temperature:

T = PV / nR

Substituting the given values, we get:

T = (707.9 kPa * 1000000 cm^3) / (0.016 kg * 287 J/kg K)

T ≈ 124.3 K

Calculating the Final Mass

The final mass of the air can be calculated by multiplying the number of moles by the molar mass of air:

m = n * M

where m is the mass and M is the molar mass.

m ≈ 0.016 kg * 28.97 g/mol ≈ 0.465 g

Conclusion

In this article, we calculated the final temperature and mass of air after being compressed to a different volume and pressure. We used the ideal gas law to relate the properties of the air and converted the units of the given values to a consistent set of units. The final temperature of the air was calculated to be approximately 124.3 K, and the final mass was calculated to be approximately 0.465 g.

References

Ideal Gas Law: PV = nRT
Molar Mass of Air: 28.97 g/mol
Conversion Factors:

1 torr = 133.322 Pascals
1 PSI = 6894.76 Pascals
1 Kelvin = 1 Celsius + 273.15

Additional Information

The ideal gas law is a fundamental principle in physics and chemistry that relates the properties of gases.
The molar mass of air is a constant value that represents the mass of one mole of air.
The conversion factors listed above are used to convert between different units of pressure and temperature.
Air at 17 C and 940 torr absolute pressure occupies 2.46 m3. Air has ag as constant of 287 J/kg K. If the gas is compressed to a volume of 1000000 cm3 and a pressure of 103 PSI, calculate a. its final temperature in K and its mass during final ====================================================================================

Q: What is the ideal gas law, and how is it used to relate the properties of gases?

A: The ideal gas law is a fundamental principle in physics and chemistry that relates the properties of gases. It is given by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

Q: What is the gas constant (R), and how is it used in the ideal gas law?

A: The gas constant (R) is a constant value that represents the ratio of the pressure of a gas to its volume and temperature. It is used in the ideal gas law to relate the properties of gases. The gas constant for air is approximately 287 J/kg K.

Q: How is the initial number of moles of air calculated using the ideal gas law?

A: The initial number of moles of air can be calculated using the ideal gas law by rearranging the equation to solve for n:

n = PV / RT

Substituting the given values, we get:

n = (124.3 kPa * 2460000 cm^3) / (287 J/kg K * 290 K)

n ≈ 0.016 kg

Q: How is the initial mass of air calculated using the number of moles and the molar mass of air?

A: The initial mass of air can be calculated by multiplying the number of moles by the molar mass of air. The molar mass of air is approximately 28.97 g/mol.

m = n * M

where m is the mass and M is the molar mass.

m ≈ 0.016 kg * 28.97 g/mol ≈ 0.465 g

Q: What is the final pressure of the air in Pascals, and how is it calculated?

A: The final pressure of the air is given as 103 PSI. We can convert this value to Pascals using the conversion factor:

1 PSI = 6894.76 Pascals

Therefore, the final pressure of the air is:

103 PSI ≈ 707.9 kPa

Q: How is the final temperature of the air calculated using the ideal gas law?

A: The final temperature of the air can be calculated using the ideal gas law by rearranging the equation to solve for T:

T = PV / nR

Substituting the given values, we get:

T = (707.9 kPa * 1000000 cm^3) / (0.016 kg * 287 J/kg K)

T ≈ 124.3 K

Q: What is the final mass of the air, and how is it calculated?

A: The final mass of the air can be calculated by multiplying the number of moles by the molar mass of air:

m = n * M

where m is the mass and M is the molar mass.

m ≈ 0.016 kg * 28.97 g/mol ≈ 0.465 g

Q: What are some common applications of the ideal gas law in real-world scenarios?

A: The ideal gas law has many applications in real-world scenarios, including:

Calculating the pressure and volume of gases in industrial processes
Determining the temperature and pressure of gases in atmospheric science
Understanding the behavior of gases in chemical reactions
Designing and optimizing systems for gas storage and transportation

Q: What are some common mistakes to avoid when using the ideal gas law?

A: Some common mistakes to avoid when using the ideal gas law include:

Failing to convert units correctly
Using the wrong value for the gas constant (R)
Not accounting for the molar mass of the gas
Not considering the effects of non-ideal behavior in real-world gases

Q: What are some additional resources for learning more about the ideal gas law and its applications?

A: Some additional resources for learning more about the ideal gas law and its applications include:

Textbooks on thermodynamics and statistical mechanics
Online tutorials and lectures on the ideal gas law
Research articles and papers on the applications of the ideal gas law
Online forums and communities for discussing the ideal gas law and its applications