A Mixture Of 1.2 G Of $N_2$ And 1.5 G Of $O_2$ Has A Pressure Of 1.0 Atm. The Partial Pressure Of Each Gas In The Mixture Is:a. $N_2=0.48 \text{ Atm}, \, O_2=0.52 \text{ Atm}$b. \$N_2=0.957 \text{ Atm}, \,

Mar 1, 2025 by ADMIN 213 views

A Mixture of Nitrogen and Oxygen: Calculating Partial Pressures

In chemistry, mixtures of gases are common and can be found in various natural and industrial processes. Understanding the behavior of these mixtures is crucial in fields such as chemical engineering, atmospheric science, and materials science. One fundamental concept in gas mixtures is the partial pressure of each component. In this article, we will explore how to calculate the partial pressure of each gas in a mixture using the ideal gas law and the concept of mole fractions.

The ideal gas law is a fundamental equation that describes the behavior of ideal gases. It is given by:

PV = nRT

where:

P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the gas constant
T is the temperature of the gas

When dealing with mixtures of gases, it is often convenient to use mole fractions instead of the number of moles. The mole fraction of a component is defined as the number of moles of that component divided by the total number of moles in the mixture. Mathematically, it can be expressed as:

x_i = n_i / N

where:

x_i is the mole fraction of component i
n_i is the number of moles of component i
N is the total number of moles in the mixture

The partial pressure of a component in a mixture can be calculated using the ideal gas law and the concept of mole fractions. The partial pressure of component i is given by:

Pi = P * xi

where:

Pi is the partial pressure of component i
P is the total pressure of the mixture
xi is the mole fraction of component i

To calculate the partial pressures, we first need to calculate the mole fractions of each component. We are given the masses of nitrogen (N2) and oxygen (O2) in the mixture: 1.2 g of N2 and 1.5 g of O2. We can calculate the number of moles of each component using their respective molar masses.

Molar Mass of N2

The molar mass of N2 is 28 g/mol.

Molar Mass of O2

The molar mass of O2 is 32 g/mol.

Calculating Number of Moles

We can calculate the number of moles of each component using the formula:

n = m / M

where:

n is the number of moles
m is the mass of the component
M is the molar mass of the component

For N2:

n_N2 = 1.2 g / 28 g/mol = 0.043 mol

For O2:

n_O2 = 1.5 g / 32 g/mol = 0.047 mol

Calculating Mole Fractions

We can now calculate the mole fractions of each component using the formula:

xi = n_i / N

where:

xi is the mole fraction of component i
n_i is the number of moles of component i
N is the total number of moles in the mixture

For N2:

x_N2 = 0.043 mol / (0.043 mol + 0.047 mol) = 0.477

For O2:

x_O2 = 0.047 mol / (0.043 mol + 0.047 mol) = 0.523

Calculating Partial Pressures

We can now calculate the partial pressures of each component using the formula:

Pi = P * xi

where:

Pi is the partial pressure of component i
P is the total pressure of the mixture
xi is the mole fraction of component i

For N2:

P_N2 = 1.0 atm * 0.477 = 0.477 atm

For O2:

P_O2 = 1.0 atm * 0.523 = 0.523 atm

In conclusion, we have calculated the partial pressures of nitrogen (N2) and oxygen (O2) in a mixture using the ideal gas law and the concept of mole fractions. We first calculated the number of moles of each component using their respective molar masses, then calculated the mole fractions of each component, and finally calculated the partial pressures of each component using the formula:

Pi = P * xi

where:

Pi is the partial pressure of component i
P is the total pressure of the mixture
xi is the mole fraction of component i

The partial pressures of N2 and O2 in the mixture are 0.477 atm and 0.523 atm, respectively.

Ideal Gas Law: PV = nRT
Mole Fractions: xi = n_i / N
Partial Pressures: Pi = P * xi

The partial pressures of gases in a mixture are an important concept in chemistry and physics. Understanding how to calculate partial pressures is crucial in fields such as chemical engineering, atmospheric science, and materials science. In this article, we have demonstrated how to calculate the partial pressures of nitrogen (N2) and oxygen (O2) in a mixture using the ideal gas law and the concept of mole fractions.

The ideal gas law assumes that the gas behaves like an ideal gas, which is not always the case in real-world scenarios. Additionally, the calculation of partial pressures assumes that the mixture is at equilibrium, which may not always be the case.

In future work, we can explore more complex scenarios, such as mixtures of gases with different molar masses and mixtures of gases with different temperatures. We can also explore the application of partial pressures in real-world scenarios, such as in chemical engineering and atmospheric science.

In conclusion, we have demonstrated how to calculate the partial pressures of nitrogen (N2) and oxygen (O2) in a mixture using the ideal gas law and the concept of mole fractions. The partial pressures of N2 and O2 in the mixture are 0.477 atm and 0.523 atm, respectively. We have also discussed the limitations of the ideal gas law and the concept of mole fractions, and have suggested future work in exploring more complex scenarios and real-world applications.
A Mixture of Nitrogen and Oxygen: Calculating Partial Pressures - Q&A

In our previous article, we explored how to calculate the partial pressures of nitrogen (N2) and oxygen (O2) in a mixture using the ideal gas law and the concept of mole fractions. In this article, we will answer some frequently asked questions (FAQs) related to the calculation of partial pressures.

Q: What is the ideal gas law?

A: The ideal gas law is a fundamental equation that describes the behavior of ideal gases. It is given by:

PV = nRT

where:

P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the gas constant
T is the temperature of the gas

Q: What is a mole fraction?

A: A mole fraction is a measure of the proportion of a component in a mixture. It is defined as the number of moles of that component divided by the total number of moles in the mixture. Mathematically, it can be expressed as:

xi = n_i / N

where:

xi is the mole fraction of component i
n_i is the number of moles of component i
N is the total number of moles in the mixture

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

A: To calculate the partial pressure of a component in a mixture, you need to know the total pressure of the mixture and the mole fraction of the component. The partial pressure of the component can be calculated using the formula:

Pi = P * xi

where:

Pi is the partial pressure of component i
P is the total pressure of the mixture
xi is the mole fraction of component i

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

A: The total pressure of a mixture is the sum of the partial pressures of all the components in the mixture. The partial pressure of a component is the pressure that the component would exert if it were the only component in the mixture.

Q: Can I use the ideal gas law to calculate the partial pressure of a component in a mixture?

A: Yes, you can use the ideal gas law to calculate the partial pressure of a component in a mixture. However, you need to know the total pressure of the mixture and the mole fraction of the component.

Q: What are some common applications of partial pressures?

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

Chemical engineering: Partial pressures are used to design and optimize chemical processes, such as distillation and absorption.
Atmospheric science: Partial pressures are used to study the composition and behavior of the atmosphere.
Materials science: Partial pressures are used to study the properties and behavior of materials, such as metals and ceramics.

In conclusion, we have answered some frequently asked questions (FAQs) related to the calculation of partial pressures. We have discussed the ideal gas law, mole fractions, and the calculation of partial pressures. We have also highlighted some common applications of partial pressures in chemistry and physics.

Ideal Gas Law: PV = nRT
Mole Fractions: xi = n_i / N
Partial Pressures: Pi = P * xi

The calculation of partial pressures is an important concept in chemistry and physics. Understanding how to calculate partial pressures is crucial in fields such as chemical engineering, atmospheric science, and materials science. In this article, we have provided a comprehensive overview of the calculation of partial pressures and have answered some frequently asked questions (FAQs) related to this topic.