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 the law of partial pressures. To find a gas's partial pressure, use the ideal gas law: $P^1=\frac{nRT}{V}$. Dalton's law relates partial pressure to fractional composition, allowing calculation of a gas's contribution to total pressure.

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 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. Remember, the total pressure experienced by a container is a direct result of the individual pressures exerted by each gas it contains.

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

In a scenario where a sample of neon gas exerts a pressure of 1.85 atmospheres in a cylinder, and nitrogen gas is present at a pressure of 500 Torr, we can determine the total pressure inside the cylinder using the law of partial pressures. This law states that the total pressure in a container is the sum of the partial pressures of each gas present.

To find the total pressure, we first need to ensure that both pressures are expressed in the same units. Neon is already in atmospheres, while nitrogen is in Torr. To convert the nitrogen pressure from Torr to atmospheres, we use the conversion factor where 1 atmosphere equals 760 Torr. Thus, the conversion for 500 Torr is calculated as follows:

\[\text{Pressure in atmospheres} = \frac{500 \text{ Torr}}{760 \text{ Torr/atm}} \approx 0.65789 \text{ atm}\]

Now, we can add the partial pressures of neon and nitrogen:

\[\text{Total Pressure} = \text{Pressure of Neon} + \text{Pressure of Nitrogen} = 1.85 \text{ atm} + 0.65789 \text{ atm} \approx 2.50789 \text{ atm}\]

When rounding the total pressure to the appropriate number of significant figures, we note that 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:

\[\text{Total Pressure} \approx 2.51 \text{ atm}\]

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

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 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, allowing us to apply the ideal gas law effectively. Understanding this relationship is crucial for analyzing gas behavior in various scientific and engineering contexts.

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

To determine the partial pressure of helium gas in a mixture with oxygen, we can utilize 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. The atomic mass of helium is approximately 4.003 g/mol, so we calculate the moles of helium as follows:

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

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:

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

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. To maintain a reasonable level of accuracy, we round the final answer to three significant figures, resulting in:

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

This calculation illustrates how the ideal gas law can be applied 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: Partial Pressure (Simplified) Concept 3

To understand the behavior of gases in a mixture, it is essential to first determine the fractional composition of a gas when its percent composition is provided. The fractional composition is calculated by dividing the percent composition of the specific gas by the total percent, which is 100%. This can be expressed with the formula:

$$ m = \frac{\text{Percent of gas}}{100\%} $$

Once the fractional composition is established, it can be utilized to calculate the partial pressure of the gas using Dalton's Law of Partial Pressures. According to this law, the partial pressure of a gas (let's denote it as gas A) is given by the 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 these concepts, one can effectively determine the partial pressures of individual gases within a mixture, enhancing the 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% nitrogen.

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

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

Partial Pressure = (Percentage of gas / 100) × Total Pressure

For carbon dioxide (CO₂):

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

For oxygen (O₂):

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

For nitrogen (N₂):

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

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

• CO₂: 7.3 atm
• O₂: 17.5 atm
• 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:

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

Here, $P_{\mathrm{total}}$ is the total pressure, and $P_1$, $P_2$, $P_3$ are the partial pressures of the individual gases.

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

To calculate the partial pressure of a gas using the ideal gas law, you need to know the number of moles of the gas (n), the gas constant (R), the temperature (T), and the volume (V) of the container. The ideal gas law is given by:

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

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

What is fractional composition and how is it used in Dalton's Law?

Fractional composition represents the ratio of the partial pressure of a gas to the total pressure in a mixture. It is calculated by dividing the percentage composition of a gas by 100%. The formula for fractional composition (m) is:

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

Using Dalton's Law, the partial pressure of a gas (P_a) can be found by multiplying its fractional composition (m_a) by the total pressure (P_total):

$P_a=m_a\times P_{\mathrm{total}}$

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

Dalton's Law of Partial Pressures is widely applicable in real-life scenarios, such as in respiratory physiology, where it helps in understanding how gases like oxygen and carbon dioxide are exchanged in the lungs. It is also used in scuba diving to calculate the partial pressures of gases in a diver's tank, ensuring safe breathing mixtures. Additionally, it is crucial in industrial processes involving gas mixtures, such as chemical manufacturing and environmental monitoring, to determine the contributions of individual gases to the total pressure.

What assumptions are made when using Dalton's Law?

When using Dalton's Law, several assumptions are made: (1) The gases in the mixture do not react with each other. (2) Each gas behaves ideally, meaning it follows the ideal gas law. (3) The volume of the container is constant. (4) The temperature is uniform throughout the container. These assumptions simplify the calculations but may not always hold true in real-world conditions, especially at high pressures or low temperatures where gases deviate from ideal behavior.