Partial Pressures of Each Gas

Oct 13, 2025 by miodeya.com 146 views

Introduction

In this problem, we are given a mixture of oxygen (O₂) and helium (He) in a 500 L container. The mass of O₂ is 75.09 g, and the mass of He is 2500 g. The mixture is kept at a temperature of $25^{\circ} C$ . We need to find the mole fraction of each gas and their partial pressures.

Mole Fraction of Each Gas

To find the mole fraction of each gas, we need to calculate the number of moles of each gas. We can use the formula:

n = m / M

where n is the number of moles, m is the mass of the gas, and M is the molar mass of the gas.

Molar Mass of O₂

The molar mass of O₂ is 32 g/mol.

Molar Mass of He

The molar mass of He is 4 g/mol.

Number of Moles of O₂

We can calculate the number of moles of O₂ as follows:

n(O₂) = m(O₂) / M(O₂) = 75.09 g / 32 g/mol = 2.346 mol

Number of Moles of He

We can calculate the number of moles of He as follows:

n(He) = m(He) / M(He) = 2500 g / 4 g/mol = 625 mol

Mole Fraction of O₂

The mole fraction of O₂ is given by:

x(O₂) = n(O₂) / (n(O₂) + n(He)) = 2.346 mol / (2.346 mol + 625 mol) = 0.0037

Mole Fraction of He

The mole fraction of He is given by:

x(He) = n(He) / (n(O₂) + n(He)) = 625 mol / (2.346 mol + 625 mol) = 0.9963

Partial Pressures of Each Gas

To find the partial pressures of each gas, we can use the ideal gas law:

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.

Temperature in Kelvin

The temperature in Kelvin is given by:

T = T(°C) + 273.15 = 25°C + 273.15 = 298.15 K

Partial Pressure of O₂

We can calculate the partial pressure of O₂ as follows:

P(O₂) = n(O₂)RT / V = 2.346 mol × 0.08206 L atm/mol K × 298.15 K / 500 L = 0.113 atm

Partial Pressure of He

We can calculate the partial pressure of He as follows:

P(He) = n(He)RT / V = 625 mol × 0.08206 L atm/mol K × 298.15 K / 500 L = 30.45 atm

Conclusion

In this problem, we have calculated the mole fraction of each gas and their partial pressures. The mole fraction of O₂ is 0.0037, and the mole fraction of He is 0.9963. The partial pressure of O₂ is 0.113 atm, and the partial pressure of He is 30.45 atm.

References

[1] Ideal Gas Law. (n.d.). Retrieved from https://en.wikipedia.org/wiki/Ideal_gas_law
[2] Molar Mass of O₂. (n.d.). Retrieved from https://www.chemicool.com/molar_mass/oxygen.html
[3] Molar Mass of He. (n.d.). Retrieved from https://www.chemicool.com/molar_mass/helium.html

Introduction
Mole Fraction of Each Gas
Molar Mass of O₂
Molar Mass of He
Number of Moles of O₂
Number of Moles of He
Mole Fraction of O₂
Mole Fraction of He
Partial Pressures of Each Gas
Temperature in Kelvin
Partial Pressure of O₂
Partial Pressure of He
Conclusion
References
Table of Contents

Introduction

Mole Fraction of Each Gas

To find the mole fraction of each gas, we need to calculate the number of moles of each gas. We can use the formula:

n = m / M

where n is the number of moles, m is the mass of the gas, and M is the molar mass of the gas.

Molar Mass of O₂

The molar mass of O₂ is 32 g/mol.

Molar Mass of He

The molar mass of He is 4 g/mol.

Number of Moles of O₂

We can calculate the number of moles of O₂ as follows:

n(O₂) = m(O₂) / M(O₂) = 75.09 g / 32 g/mol = 2.346 mol

Number of Moles of He

We can calculate the number of moles of He as follows:

n(He) = m(He) / M(He) = 2500 g / 4 g/mol = 625 mol

Mole Fraction of O₂

The mole fraction of O₂ is given by:

x(O₂) = n(O₂) / (n(O₂) + n(He)) = 2.346 mol / (2.346 mol + 625 mol) = 0.0037

Mole Fraction of He

The mole fraction of He is given by:

x(He) = n(He) / (n(O₂) + n(He)) = 625 mol / (2.346 mol + 625 mol) = 0.9963

Partial Pressures of Each Gas

To find the partial pressures of each gas, we can use the ideal gas law:

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.

Temperature in Kelvin

The temperature in Kelvin is given by:

T = T(°C) + 273.15 = 25°C + 273.15 = 298.15 K

Partial Pressure of O₂

We can calculate the partial pressure of O₂ as follows:

P(O₂) = n(O₂)RT / V = 2.346 mol × 0.08206 L atm/mol K × 298.15 K / 500 L = 0.113 atm

Partial Pressure of He

We can calculate the partial pressure of He as follows:

P(He) = n(He)RT / V = 625 mol × 0.08206 L atm/mol K × 298.15 K / 500 L = 30.45 atm

Q&A

Q: What is the mole fraction of O₂ in the mixture?

A: The mole fraction of O₂ is 0.0037.

Q: What is the mole fraction of He in the mixture?

A: The mole fraction of He is 0.9963.

Q: What is the partial pressure of O₂ in the mixture?

A: The partial pressure of O₂ is 0.113 atm.

Q: What is the partial pressure of He in the mixture?

A: The partial pressure of He is 30.45 atm.

Q: What is the total pressure of the mixture?

A: The total pressure of the mixture is the sum of the partial pressures of O₂ and He, which is 30.58 atm.

Q: What is the effect of increasing the temperature on the partial pressures of the gases?

A: Increasing the temperature will increase the partial pressures of both O₂ and He.

Q: What is the effect of increasing the volume of the container on the partial pressures of the gases?

A: Increasing the volume of the container will decrease the partial pressures of both O₂ and He.

Conclusion

References

[1] Ideal Gas Law. (n.d.). Retrieved from https://en.wikipedia.org/wiki/Ideal_gas_law
[2] Molar Mass of O₂. (n.d.). Retrieved from https://www.chemicool.com/molar_mass/oxygen.html
[3] Molar Mass of He. (n.d.). Retrieved from https://www.chemicool.com/molar_mass/helium.html

Introduction
Mole Fraction of Each Gas
Molar Mass of O₂
Molar Mass of He
Number of Moles of O₂
Number of Moles of He
Mole Fraction of O₂
Mole Fraction of He
Partial Pressures of Each Gas
Temperature in Kelvin
Partial Pressure of O₂
Partial Pressure of He
Q&A
Conclusion
References
Table of Contents