Partial Pressure: Videos & Practice Problems

Partial pressure is the individual pressure exerted by a gas within a mixture, and the total pressure inside a container is the sum of the partial pressures of each gas, as stated by Dalton's Law of Partial Pressures. To calculate the partial pressure of a specific gas, one can use the ideal gas law if the gas behaves ideally. The formula involves the number of moles of the gas, the gas constant, the temperature, and the volume of the container. Additionally, Dalton's Law allows for the use of mole fraction to find a gas's partial pressure by multiplying the mole fraction by the total pressure. Understanding these concepts is crucial for analyzing gas mixtures and their behaviors under various conditions.

Law of Partial Pressures

Partial pressure refers to the pressure that an individual gas contributes to the total pressure in a mixture of gases. In a container filled with unreacting gases, the total pressure can be determined by summing the partial pressures of each gas present. This concept is encapsulated in the law of partial pressures, which states that the total pressure (P_total) is equal to the sum of the partial pressures of all the gases in the mixture.

Mathematically, this can be expressed as:

P_total = P_{gas 1} + P_{gas 2} + P_{gas 3} + ...

Understanding this principle is crucial for analyzing gas behavior in various scientific and engineering applications, as it highlights how each gas contributes to the overall pressure within a system. This foundational knowledge is essential for further studies in thermodynamics and gas laws.

Total Pressure Example

In this scenario, we are analyzing the total pressure exerted by a mixture of gases in a cylinder, specifically neon and nitrogen. According to the law of partial pressures, the total pressure in a container is the sum of the partial pressures of each gas present. Here, the neon gas exerts a pressure of 1.85 atmospheres, while the nitrogen gas exerts a pressure of 500 Torr.

To find the total pressure, we first need to ensure that both pressures are expressed in the same unit. Since atmospheres is a standard unit for pressure, we will convert the nitrogen pressure from Torr to atmospheres. The conversion factor is that 1 atmosphere is equivalent to 760 Torr. Therefore, to convert 500 Torr to atmospheres, we use the formula:

Pressure (atm) = Pressure (Torr) × (1 atm / 760 Torr)

Substituting the values, we have:

Pressure (atm) = 500 Torr × (1 atm / 760 Torr) ≈ 0.65789 atm

Now, we can calculate the total pressure in the cylinder by adding the partial pressures of neon and nitrogen:

Total Pressure = Pressure (Neon) + Pressure (Nitrogen)

Total Pressure = 1.85 atm + 0.65789 atm ≈ 2.50789 atm

When rounding the final answer, we consider significant figures. The pressure of neon has three significant figures, while the pressure of nitrogen has only one. To maintain consistency and accuracy, we round the total pressure to three significant figures, resulting in:

Total Pressure ≈ 2.51 atm

This example illustrates the importance of unit conversion and significant figures in calculating total pressure in gas mixtures.

Partial Pressure Calculation

In a container filled with multiple gases, the total pressure is the sum of the partial pressures of each gas present. To determine the partial pressure of a specific gas, we can utilize the ideal gas law, which is expressed as:

$$ P = \frac{nRT}{V} $$

In this equation, P represents the partial pressure of the gas, n is the number of moles of the gas, R is the ideal gas constant, T is the absolute temperature of the gas in Kelvin, and V is the volume of the container. By isolating the gas of interest, referred to as gas 1, we can calculate its partial pressure using the known values of its moles, temperature, and the volume of the container.

This approach assumes that the gas behaves ideally, meaning it follows the ideal gas law without deviations. Understanding this relationship is crucial for analyzing gas mixtures and their behaviors under various conditions.

Partial Pressure Calculation Example

To determine the partial pressure of helium gas in a mixture with oxygen, we can apply the ideal gas law, which is expressed as:

\( P = \frac{nRT}{V} \)

Where:

• P = pressure of the gas (in atmospheres)
• n = number of moles of the gas
• R = ideal gas constant, approximately \( 0.08206 \, \text{L} \cdot \text{atm} / (\text{mol} \cdot \text{K}) \)
• T = temperature in Kelvin
• V = volume of the gas (in liters)

In this scenario, we have 12 grams of helium and 20 grams of oxygen in a 5-liter cylinder at a temperature of 30 degrees Celsius. Since we are only interested in the partial pressure of helium, we first need to convert the mass of helium to moles. The atomic mass of helium is approximately 4.003 grams per mole, so we calculate the moles of helium as follows:

\( n_{\text{He}} = \frac{12 \, \text{g}}{4.003 \, \text{g/mol}} \approx 2.998 \, \text{mol} \)

Next, we convert the temperature from Celsius to Kelvin:

\( T = 30 \, \text{°C} + 273.15 = 303.15 \, \text{K} \)

Now, we can substitute the values into the ideal gas law formula to find the partial pressure of helium:

\( P_{\text{He}} = \frac{(2.998 \, \text{mol}) \times (0.08206 \, \text{L} \cdot \text{atm} / (\text{mol} \cdot \text{K})) \times (303.15 \, \text{K})}{5 \, \text{L}} \)

Calculating this gives:

\( P_{\text{He}} \approx 14.9149 \, \text{atm} \)

When considering significant figures, we observe that the values provided have varying degrees of precision. The most appropriate representation of the pressure, maintaining three significant figures, is:

\( P_{\text{He}} \approx 14.9 \, \text{atm} \)

This calculation illustrates how the ideal gas law can be utilized to find the partial pressure of a specific gas in a mixture, emphasizing the importance of moles, temperature, and volume in the process.

Dalton's Law and Partial Pressure

Dalton's Law of Partial Pressures states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each individual gas in the mixture. The partial pressure of a specific gas can be calculated using the formula:

\( P_1 = X_1 \times P_{total} \)

In this equation, \( P_1 \) represents the partial pressure of gas 1, \( X_1 \) is the mole fraction of gas 1, and \( P_{total} \) is the total pressure of the gas mixture. The mole fraction is a crucial concept in this calculation, defined as the ratio of the number of moles of a specific gas to the total number of moles of all gases present in the mixture.

To calculate the mole fraction, use the formula:

\( X_1 = \frac{n_1}{n_{total}} \)

where \( n_1 \) is the number of moles of gas 1 and \( n_{total} \) is the total number of moles of all gases in the mixture. Understanding how to determine the mole fraction is essential for applying Dalton's Law effectively, as it allows for accurate calculations of partial pressures in various gas mixtures.

Mole Fraction and Partial Pressure Calculation Example

To calculate the mole fraction and partial pressure of oxygen (O₂) in a gas mixture, we start with the given masses of the gases: 16.7 grams of O₂, 8.1 grams of H₂, and 35.2 grams of N₂. The total pressure of the mixture is 0.83 atmospheres. The mole fraction of a gas is defined as the number of moles of that gas divided by the total number of moles of all gases present.

First, we need to convert the masses of each gas into moles using their respective molar masses:

• For O₂: The molar mass is 32 g/mol, so the number of moles is calculated as follows: \[ \text{moles of O}_2 = \frac{16.7 \text{ g}}{32 \text{ g/mol}} = 0.5219 \text{ moles} \]
• For H₂: The molar mass is 2.016 g/mol, so: \[ \text{moles of H}_2 = \frac{8.1 \text{ g}}{2.016 \text{ g/mol}} = 4.018 \text{ moles} \]
• For N₂: The molar mass is 28.02 g/mol, so: \[ \text{moles of N}_2 = \frac{35.2 \text{ g}}{28.02 \text{ g/mol}} = 1.2562 \text{ moles} \]

Next, we calculate the total number of moles in the mixture:

\[\text{Total moles} = 0.5219 + 4.018 + 1.2562 = 5.7961 \text{ moles}\]

Now, we can find the mole fraction of O₂:

\[\text{Mole fraction of O}_2 = \frac{0.5219 \text{ moles}}{5.7961 \text{ moles}} = 0.0900\]

With the mole fraction determined, we can now calculate the partial pressure of O₂ using Dalton's Law of Partial Pressures, which states that the partial pressure of a gas is equal to its mole fraction multiplied by the total pressure:

\[\text{Partial pressure of O}_2 = \text{Mole fraction of O}_2 \times \text{Total pressure} = 0.0900 \times 0.83 \text{ atm} = 0.075 \text{ atm}\]

In summary, the mole fraction of O₂ in the mixture is 0.0900, and its partial pressure is 0.075 atmospheres. Remember that the mole fraction is a unitless quantity, and the significant figures in the final answer are determined by the values with the least number of significant figures in the calculations, which in this case is two.

A sample of 3.51 g argon and an unknown amount of oxygen are mixed in a container at room temperature. The partial pressure of argon was calculated as 71.0 torr and the partial pressure of oxygen as 188 torr. What is the mass of the oxygen within the container?

• A. 4.27 g
• B. 6.18 g
• C. 7.44 g
• D. 9.16 g
• E. 15.2 g

Answer: (C)

A gas mixture contains 72.8% chlorine and 27.2% neon by mass. What is the partial pressure of neon in the mixture if the total pressure is recorded as 809 mmHg?

• A. 260 mmHg
• B. 289 mmHg
• C. 320 mmHg
• D. 392 mmHg
• E. 459 mmHg

Answer: (E)

Here’s what students ask on this topic:

How can one find partial pressure?

Partial pressure is the pressure that a gas in a mixture of gases would exert if it alone occupied the entire volume of the mixture at the same temperature. To find the partial pressure of a gas, you can use Dalton's Law of Partial Pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.

The formula to calculate the partial pressure of a gas is:

$P_{\mathrm{gas}}=\left(X_{\mathrm{gas}}\right)P_{\mathrm{total}}$

Where:

• Pgas is the partial pressure of the gas you're interested in.
• Xgas is the mole fraction of the gas in the mixture, which is the ratio of the number of moles of that gas to the total number of moles of all gases in the mixture.
• Ptotal is the total pressure of the gas mixture.

For example, if you have a gas mixture in a container and you know the total pressure of the mixture and the mole fraction of each gas, you can calculate the partial pressure of each gas using the formula above. Remember that the temperature and volume of the container are constant when using this formula.

How do you calculate partial pressure?

To calculate the partial pressure of a gas in a mixture, you can use Dalton's Law of Partial Pressures. According to this law, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases. The partial pressure of each gas is proportional to its mole fraction in the mixture.

Here's how you can calculate it:

1. Determine the mole fraction of the gas: Divide the number of moles of the gas by the total number of moles of all gases in the mixture.

Mole Fraction (_Xgas) = moles of gas / total moles of all gases

2. Multiply the mole fraction by the total pressure of the gas mixture to find the partial pressure:

Partial Pressure (_Pgas) = Mole Fraction (_Xgas) * Total Pressure (_Ptotal)

For example, if you have a mixture of oxygen and nitrogen with a total pressure of 1 atmosphere (atm), and the mole fraction of oxygen is 0.21, the partial pressure of oxygen would be:

_PO2 = 0.21 * 1 atm = 0.21 atm

Remember that the total pressure must be known, and the gases should not react with each other for this calculation to be valid.

What is partial pressure?

Partial pressure is a concept in chemistry and physics that refers to the pressure that a single gas in a mixture of gases would exert if it alone occupied the entire volume of the mixture at the same temperature. This is an important concept in understanding gas behavior and is based on Dalton's Law of Partial Pressures, which states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases.

To put it simply, imagine you have a container filled with a mixture of oxygen and nitrogen. The partial pressure of oxygen is the pressure it would exert if it were the only gas in the container. The same goes for nitrogen. So, if you know the partial pressures of all the gases in a mixture, you can add them up to find the total pressure. This principle is crucial in various scientific fields, including respiratory physiology, where it helps to understand how gases are exchanged in the lungs.