Calculating the Total Pressure

Oct 13, 2025 by miodeya.com 148 views

Introduction

In chemistry, a gas cylinder can contain a mixture of different gases, each with its own partial pressure. The partial pressure of a gas is the pressure that the gas would exert if it were the only gas present in the cylinder. In this article, we will explore the concept of partial pressures and how to calculate the total pressure of a gas mixture using the given partial pressures of five gases: nitrogen (N2), oxygen (O2), argon (Ar), helium (He), and an unknown gas.

Partial Pressures and Dalton's Law

Dalton's Law states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each gas. Mathematically, this can be expressed as:

P_total = P1 + P2 + P3 + ... + Pn

where P_total is the total pressure of the gas mixture, and P1, P2, P3, ..., Pn are the partial pressures of each gas.

Calculating the Total Pressure

Given the partial pressures of the five gases in the gas cylinder, we can calculate the total pressure using Dalton's Law. The partial pressures are:

N2: 3.00 atm
O2: 1.80 atm
Ar: 0.29 atm
He: 0.18 atm
Unknown gas: 0.10 atm

To calculate the total pressure, we simply add the partial pressures of each gas:

P_total = 3.00 atm + 1.80 atm + 0.29 atm + 0.18 atm + 0.10 atm P_total = 5.37 atm

Understanding the Mole Fraction

The mole fraction of a gas is the ratio of the number of moles of that gas to the total number of moles of all gases in the mixture. The mole fraction can be calculated using the following formula:

X_i = n_i / (n_1 + n_2 + n_3 + ... + n_n)

where X_i is the mole fraction of gas i, and n_i is the number of moles of gas i.

Calculating the Mole Fraction of Each Gas

To calculate the mole fraction of each gas, we need to know the number of moles of each gas. We can calculate the number of moles using 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.

Assuming a temperature of 25°C (298 K) and a volume of 1 L, we can calculate the number of moles of each gas:

N2: n = PV / RT = (3.00 atm * 1 L) / (0.08206 L atm/mol K * 298 K) = 0.124 mol
O2: n = PV / RT = (1.80 atm * 1 L) / (0.08206 L atm/mol K * 298 K) = 0.071 mol
Ar: n = PV / RT = (0.29 atm * 1 L) / (0.08206 L atm/mol K * 298 K) = 0.011 mol
He: n = PV / RT = (0.18 atm * 1 L) / (0.08206 L atm/mol K * 298 K) = 0.007 mol
Unknown gas: n = PV / RT = (0.10 atm * 1 L) / (0.08206 L atm/mol K * 298 K) = 0.004 mol

Now we can calculate the mole fraction of each gas:

N2: X_N2 = n_N2 / (n_N2 + n_O2 + n_Ar + n_He + n_unknown) = 0.124 mol / (0.124 + 0.071 + 0.011 + 0.007 + 0.004) = 0.43
O2: X_O2 = n_O2 / (n_N2 + n_O2 + n_Ar + n_He + n_unknown) = 0.071 mol / (0.124 + 0.071 + 0.011 + 0.007 + 0.004) = 0.23
Ar: X_Ar = n_Ar / (n_N2 + n_O2 + n_Ar + n_He + n_unknown) = 0.011 mol / (0.124 + 0.071 + 0.011 + 0.007 + 0.004) = 0.04
He: X_He = n_He / (n_N2 + n_O2 + n_Ar + n_He + n_unknown) = 0.007 mol / (0.124 + 0.071 + 0.011 + 0.007 + 0.004) = 0.02
Unknown gas: X_unknown = n_unknown / (n_N2 + n_O2 + n_Ar + n_He + n_unknown) = 0.004 mol / (0.124 + 0.071 + 0.011 + 0.007 + 0.004) = 0.01

Conclusion

In conclusion, we have calculated the total pressure of a gas mixture using Dalton's Law and the given partial pressures of five gases. We have also calculated the mole fraction of each gas using the ideal gas law and the number of moles of each gas. The results show that the total pressure of the gas mixture is 5.37 atm, and the mole fraction of each gas is 0.43 (N2), 0.23 (O2), 0.04 (Ar), 0.02 (He), and 0.01 (unknown gas).

References

Dalton, J. (1801). A New System of Chemical Philosophy. London: Bickerstaff.
Ideal Gas Law. (n.d.). Retrieved from https://en.wikipedia.org/wiki/Ideal_gas_law
Mole Fraction. (n.d.). Retrieved from https://en.wikipedia.org/wiki/Mole_fraction
Frequently Asked Questions (FAQs) about Partial Pressures and Gas Mixtures ================================================================================

Q: What is the difference between partial pressure and total pressure?

A: The partial pressure of a gas is the pressure that the gas would exert if it were the only gas present in the mixture. The total pressure of a gas mixture is the sum of the partial pressures of each gas.

Q: How do I calculate the partial pressure of a gas in a mixture?

A: To calculate the partial pressure of a gas in a mixture, you need to know the total pressure of the mixture and the mole fraction of the gas. You can use the following formula:

P_i = X_i * P_total

where P_i is the partial pressure of gas i, X_i is the mole fraction of gas i, and P_total is the total pressure of the mixture.

Q: What is the mole fraction of a gas in a mixture?

A: The mole fraction of a gas in a mixture is the ratio of the number of moles of that gas to the total number of moles of all gases in the mixture. It can be calculated using the following formula:

X_i = n_i / (n_1 + n_2 + n_3 + ... + n_n)

where X_i is the mole fraction of gas i, n_i is the number of moles of gas i, and n_1, n_2, n_3, ..., n_n are the number of moles of each gas in the mixture.

Q: How do I calculate the number of moles of a gas in a mixture?

A: To calculate the number of moles of a gas in a mixture, you need to know the pressure, volume, and temperature of the gas. You can use the ideal gas law to calculate the number of moles:

n = PV / RT

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

Q: What is the significance of partial pressures in a gas mixture?

A: Partial pressures are important in a gas mixture because they determine the behavior of each gas in the mixture. For example, the partial pressure of a gas can affect its boiling point, melting point, and solubility in a solvent.

Q: Can I use partial pressures to predict the behavior of a gas mixture?

A: Yes, you can use partial pressures to predict the behavior of a gas mixture. By knowing the partial pressures of each gas, you can predict the behavior of the mixture as a whole. For example, you can use partial pressures to predict the boiling point, melting point, and solubility of a gas mixture.

Q: What are some common applications of partial pressures in chemistry?

A: Partial pressures have many applications in chemistry, including:

Calculating the boiling point and melting point of a gas mixture
Predicting the solubility of a gas in a solvent
Determining the behavior of a gas mixture in a chemical reaction
Calculating the partial pressure of a gas in a mixture

Q: How do I calculate the partial pressure of a gas in a mixture using Dalton's Law?

A: To calculate the partial pressure of a gas in a mixture using Dalton's Law, you need to know the total pressure of the mixture and the mole fraction of the gas. You can use the following formula:

P_i = X_i * P_total

where P_i is the partial pressure of gas i, X_i is the mole fraction of gas i, and P_total is the total pressure of the mixture.

Q: What is Dalton's Law?

A: Dalton's Law states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each gas. Mathematically, this can be expressed as:

P_total = P1 + P2 + P3 + ... + Pn

where P_total is the total pressure of the mixture, and P1, P2, P3, ..., Pn are the partial pressures of each gas.

Q: Can I use Dalton's Law to calculate the partial pressure of a gas in a mixture?

A: Yes, you can use Dalton's Law to calculate the partial pressure of a gas in a mixture. By knowing the total pressure of the mixture and the partial pressures of each gas, you can calculate the partial pressure of the gas using the following formula:

P_i = P_total - (P1 + P2 + P3 + ... + Pn)

where P_i is the partial pressure of gas i, P_total is the total pressure of the mixture, and P1, P2, P3, ..., Pn are the partial pressures of each gas.