Dalton's Law: Partial Pressure (Simplified): Videos & Practice Problems

Partial pressure refers to the pressure exerted by an individual gas in a mixture, contributing to the total pressure in a container, as described by Dalton's law of partial pressures. The partial pressure of a gas can be calculated using the ideal gas law, where $P=\frac{nRT}{V}$. Additionally, the fractional composition of a gas aids in determining its partial pressure through the formula: $P=fP\_\mathrm{total}$, where f is the fractional composition.

Dalton's Law: Partial Pressure (Simplified) Concept 1

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 is the cumulative effect of the partial pressures of each gas present. This relationship is encapsulated in the law of partial pressures, which states that the total pressure (P_total) in a container can be calculated by summing the partial pressures of all the gases involved.

Mathematically, this can be expressed as:

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

Understanding this concept 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 principle is fundamental in fields such as chemistry, physics, and environmental science, where gas mixtures are common.

Dalton's Law: Partial Pressure (Simplified) Example 1

In this scenario, we are analyzing the total pressure exerted by a mixture of gases, specifically neon and nitrogen, within a cylinder. 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.

Dalton's Law: Partial Pressure (Simplified) Concept 2

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 one gas, referred to as gas 1, we can calculate its partial pressure using its specific moles, the temperature of the system, 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 applications in chemistry and physics, particularly in scenarios involving gas mixtures and reactions.

Dalton's Law: Partial Pressure (Simplified) Example 2

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. First, we need to convert the mass of helium to moles:

Using the atomic mass of helium, which is approximately \(4.003 \, \text{g/mol}\), we calculate the moles of helium:

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

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:

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

Calculating this gives:

\( P \approx 14.9149 \, \text{atm} \)

When considering significant figures, we observe that the values provided have varying degrees of precision. To maintain consistency, we round the final answer to three significant figures:

\( P \approx 14.9 \, \text{atm} \)

This result indicates that the partial pressure of helium in the cylinder is approximately 14.9 atmospheres. Remember, the ideal gas law is a powerful tool for calculating the behavior of gases under various conditions, and understanding how to manipulate the equation is essential for solving related problems.

Dalton's Law: Partial Pressure (Simplified) Concept 3

To understand the behavior of gases in a mixture, it's essential to grasp the concept of fractional composition. This term refers to the proportion of a specific gas in relation to the total composition of the gas mixture. The formula for calculating fractional composition is straightforward: it is the percentage of the gas of interest divided by the total percentage, which is typically 100%. This can be expressed mathematically as:

$$ \text{Fractional Composition} (m) = \frac{\text{Percentage of Gas}}{100\%} $$

Once the fractional composition is determined, it can be utilized to find the partial pressure of that gas within the mixture. This is where Dalton's Law of Partial Pressures comes into play. According to Dalton's Law, the partial pressure of a specific gas (let's denote it as gas A) can be calculated using the following equation:

$$ P_A = m_A \times P_{\text{total}} $$

In this equation, \( P_A \) represents the partial pressure of gas A, \( m_A \) is the fractional composition of gas A, and \( P_{\text{total}} \) is the total pressure of the gas mixture. By applying this law, one can effectively determine the contribution of each gas to the overall pressure in a container, facilitating a deeper understanding of gas behavior in various conditions.

Dalton's Law: Partial Pressure (Simplified) Example 3

In a gas mixture used for calibrating blood gas analyzers, the composition includes 5% carbon dioxide (CO₂), 12% oxygen (O₂), and the remainder nitrogen (N₂). To determine the partial pressures of each gas component, we first calculate the percentage of nitrogen by subtracting the percentages of CO₂ and O₂ from 100%:

Percentage of nitrogen = 100% - (5% + 12%) = 83%

Next, we can find the partial pressure of each gas using Dalton's Law of Partial Pressures, which states that the partial pressure of a gas in a mixture is equal to the total pressure multiplied by the fractional composition of that gas. The total pressure of the gas mixture is 146 atmospheres.

The formula for calculating the partial pressure of each gas is:

Partial Pressure = (Fractional Composition) × (Total Pressure)

For carbon dioxide (CO₂):

Partial Pressure of CO₂ = (5% / 100) × 146 atm = 0.05 × 146 atm = 7.3 atm

For oxygen (O₂):

Partial Pressure of O₂ = (12% / 100) × 146 atm = 0.12 × 146 atm = 17.5 atm

For nitrogen (N₂):

Partial Pressure of N₂ = (83% / 100) × 146 atm = 0.83 × 146 atm = 121.2 atm

In summary, the partial pressures of the gas components in the mixture are approximately:

• Carbon Dioxide (CO₂): 7.3 atm
• Oxygen (O₂): 17.5 atm
• Nitrogen (N₂): 121.2 atm

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. 220 mmHg
• B. 242 mmHg
• C. 588 mmHg
• D. 183 mmHg

Answer: (A)

The partial pressure of N₂ in the air is 593 mmHg at 1 atm. What is the partial pressure of N₂ in a bubble of air a scuba diver breathes when he is 66 ft below the surface of the water where the pressure is 3.00 atm?

• A. 2.34 mmHg
• B. 1779 mmHg
• C. 593 mmHg
• D. 2.28×10³ mmHg
• E. 7.02 mmHg

Answer: (B)

Here’s what students ask on this topic:

What is Dalton's Law of Partial Pressures?

Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of non-reacting gases in a container is equal to the sum of the partial pressures of each individual gas. Mathematically, it can be expressed as:

$P_{\text{total}}=P_1+P_2+P_3+...$

where $P_1$ is the partial pressure of gas 1, $P_2$ is the partial pressure of gas 2, and so on. Each gas in the mixture contributes to the total pressure proportionally to its amount.

How do you calculate the partial pressure of a gas using the ideal gas law?

The partial pressure of a gas in a mixture can be calculated using the ideal gas law, which is:

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

Here, $P$ is the partial pressure of the gas, $n$ is the number of moles of the gas, $R$ is the gas constant, $T$ is the temperature in Kelvin, and $V$ is the volume of the container. By knowing the moles, temperature, and volume, you can determine the partial pressure of the gas.

What is fractional composition and how is it used to calculate partial pressure?

Fractional composition represents the ratio of the amount of a particular gas to the total amount of gases in a mixture. It is calculated by dividing the percentage composition of the gas by 100%. The formula is:

$f=\frac{\mathrm{percentage}}{100}$

To find the partial pressure of a gas using its fractional composition, you multiply the fractional composition by the total pressure:

$P_a=f{P}_{\text{total}}$

where $P_a$ is the partial pressure of gas a, $f$ is the fractional composition, and $P_{\text{total}}$ is the total pressure.

How does Dalton's Law apply to real-life situations?

Dalton's Law of Partial Pressures is applicable in various real-life situations, such as calculating the pressure of gases in scuba diving tanks, determining the composition of gases in the atmosphere, and in medical applications like anesthesia delivery. For example, in scuba diving, knowing the partial pressures of oxygen and nitrogen is crucial to avoid conditions like oxygen toxicity and nitrogen narcosis. In the atmosphere, Dalton's Law helps in understanding how different gases like oxygen, nitrogen, and carbon dioxide contribute to the total atmospheric pressure.

What assumptions are made when using Dalton's Law of Partial Pressures?

When using Dalton's Law of Partial Pressures, several assumptions are made: (1) The gases in the mixture do not react with each other. (2) The gases behave ideally, meaning they follow the ideal gas law. (3) The volume of the individual gas molecules is negligible compared to the volume of the container. (4) There are no intermolecular forces between the gas molecules. These assumptions simplify the calculations but may not always hold true in real-world scenarios, especially at high pressures or low temperatures.