Question

What is the total pressure of a gas mixture containing these partial pressures: \(\mathrm{PN}_{2}=0.78 \mathrm{~atm}\) \(\mathrm{PH}_{2}=0.33 \mathrm{~atm}\), and \(\mathrm{PO}_{2}=1.59\) atm?

Short answer

The total pressure of the gas mixture is 2.70 atm.

Step-by-step solution

Define Dalton's Law of Partial Pressures

Dalton's Law of Partial Pressures states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture. This can be expressed as follows: \[ P_{total} = P_{N_2} + P_{H_2} + P_{O_2} \]

Identify the Given Partial Pressures

From the problem, we know the partial pressures are: - \( P_{N_2} = 0.78 \) atm- \( P_{H_2} = 0.33 \) atm- \( P_{O_2} = 1.59 \) atm.

Substitute the Values into the Equation

Insert the given partial pressures into the equation for total pressure:\[ P_{total} = 0.78\, \text{atm} + 0.33\, \text{atm} + 1.59\, \text{atm} \]

Calculate the Total Pressure

Add the partial pressures together:\[ P_{total} = 0.78 + 0.33 + 1.59 = 2.70 \]\text{atm}.

Key concepts

Dalton's Law

Dalton's Law is a fundamental principle in chemistry that relates to gas mixtures and their 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 in the mixture. A partial pressure is the pressure that a single gas in a mixture would exert if it occupied the entire volume by itself. This is crucial for understanding how different gases interact in a confined space.
This concept helps scientists and students calculate how gases behave when combined. It's widely used in real-world applications, such as breathing environments for astronauts or divers, where multiple gases are combined to create a breathable atmosphere. Understanding Dalton's Law is integral for predicting and adjusting these environments to be safe and effective.

Gas Mixture

A gas mixture consists of two or more different gases occupying the same physical space. In a gas mixture, each type of gas retains its individual properties, such as chemical behavior and partial pressure. The total behavior of the gas mixture is influenced by the behavior of each component gas.
For example, when you have a gas mixture containing nitrogen ( 2), hydrogen ( H2), and oxygen ( O2), each gas contributes to the overall pressure based on its partial pressure. These gases can coexist without chemically reacting, provided they are stable under the conditions given.
Gas mixtures are commonly encountered in both natural and industrial settings. Our atmosphere itself is a complex gas mixture primarily of nitrogen, oxygen, carbon dioxide, and other trace gases, which makes understanding gas mixtures essential for various scientific and environmental studies.

Total Pressure

The concept of total pressure in a gas mixture is derived from Dalton's Law. It refers to the total force exerted by the gas mixture on the walls of its container. To find the total pressure of a gas mixture, you sum up all the partial pressures of gases present in the system.
In practice, you calculate the total pressure using the equation: \[ P_{total} = P_{gas1} + P_{gas2} + \ldots + P_{gasn} \]
Where each \(P_{gas}\) represents the partial pressure of an individual gas component. In our example exercise, the total pressure was calculated by adding the given partial pressures: 0.78 atm for nitrogen, 0.33 atm for hydrogen, and 1.59 atm for oxygen, resulting in a total pressure of 2.70 atm.
This principle is crucial for various scientific calculations, such as predicting how gases will behave under different conditions and ensuring the correct pressure levels are maintained in controlled environments.

Atm (Atmosphere)

The term "atm" stands for "atmosphere," a unit of measurement used to describe pressure. In scientific terms, 1 atmosphere is defined as being precisely equal to 101,325 Pascal, another unit of pressure. It is equivalent to the average atmospheric pressure at sea level on Earth.
Atmosphere as a unit is significant in chemistry, physics, and various engineering fields. When measuring gas pressures, using "atm" provides a relatable scale since it compares pressures to something experienced in everyday life. If someone uses atm to describe pressure, it suggests how much force a gas mixture exerts in terms of the sea-level atmospheric pressure.
Understanding how to use and convert this unit is important for students and professionals working in fields that involve gas behavior, such as aerospace engineering, meteorology, and environmental science. It allows you to draw comparisons between laboratory conditions and real-world environments, ensuring accuracy and reliability in measurements and calculations.