Question

Air contains \(79 \% \mathrm{~N}_{2}\) and \(21 \% \mathrm{O}_{2}\) by volume. If the barometric pressure is \(750 \mathrm{~mm}\) IIg the partial pressure of oxygen is (1) \(157.7 \mathrm{~mm}\) of IIg (2) \(175.5 \mathrm{~mm}\) of IIg (3) \(315.0 \mathrm{~mm}\) of IIg (4) Nonc

Short answer

The partial pressure of oxygen is 157.5 mm Hg, closest to option (1) 157.7 mm Hg.

Step-by-step solution

Identify Given Data

We know that the air contains 21% oxygen by volume and the barometric pressure is given as 750 mm Hg. We need to find the partial pressure of oxygen.

Understand Dalton's Law of Partial Pressures

Dalton's Law states that the total pressure of a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases. The partial pressure of a gas in a mixture is given by the product of its fraction in the mixture and the total pressure.

Calculate the Partial Pressure of Oxygen

The partial pressure of oxygen can be calculated using the fraction of oxygen in the air and the total pressure. The fraction of oxygen is 21%, or 0.21. Multiply this fraction by the total pressure: \[ P_{O_2} = 0.21 \times 750 \text{ mm Hg} \]

Multiply and Find the Result

Perform the multiplication to find the partial pressure of oxygen: \[ P_{O_2} = 0.21 \times 750 = 157.5 \text{ mm Hg} \]

Key concepts

Partial Pressure Calculation

Dalton's Law of Partial Pressures helps us understand how individual gases in a mixture contribute to the total pressure. The partial pressure of a gas in a mixture is determined by the gas's volume fraction and the total pressure of the mixture. For example, in the given exercise, we know that oxygen makes up 21% of the air by volume and the barometric pressure is 750 mm Hg.
To find the partial pressure of oxygen \(P_{O_2}\), you simply multiply the fraction of oxygen by the total barometric pressure:
\( P_{O_2} = 0.21 \times 750 \text{ mm Hg} = 157.5 \text{ mm Hg} \)
Here 0.21 is the fractional volume of oxygen (21%). This calculation shows how each gas in the air contributes to the overall atmospheric pressure measured at 750 mm Hg.

Barometric Pressure

Barometric pressure, also known as atmospheric pressure, is the pressure exerted by the weight of the Earth's atmosphere. It's a key concept when working with gas laws. Barometric pressure is often measured in millimeters of mercury (mm Hg) using a barometer.
At sea level, the standard barometric pressure is about 760 mm Hg. Thus, when we say the barometric pressure is 750 mm Hg, it indicates the pressure of the atmosphere exerted on everything within it.
It's crucial to understand this because when we talk about partial pressures, like in our example with oxygen, the barometric pressure provides the baseline total pressure from which we calculate the specific contributions of individual gases.
Key points to remember about barometric pressure:

• Barometric pressure changes with altitude; it is lower at higher altitudes.
• Weather patterns can also cause fluctuations in barometric pressure.
• It is essential for calculating gas behavior in different environments.

Gas Laws

The gas laws are a set of laws that describe the behavior of gases and their relationships between pressure, volume, and temperature. Dalton's Law of Partial Pressures, used in the example, is one such fundamental gas law.
Here are some core gas laws:

• Boyle's Law: For a given mass of gas at constant temperature, the volume of the gas is inversely proportional to its pressure (\( PV = \text{constant} \)).
• Charles's Law: The volume of a gas is directly proportional to its temperature (in Kelvin) at constant pressure (\( V/T = \text{constant} \)).
• Avogadro's Law: Equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules (\( V/n = \text{constant} \)).
• Dalton's Law: As we've seen, the total pressure of a mixture of gases is the sum of each individual gas's partial pressure.

Understanding these gas laws is essential for solving many real-world problems involving gases. For example, knowing Dalton's Law allows us to calculate the partial pressures of gases in different environments, which is critical in fields like chemistry, environmental science, and medicine.