Problem 53 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

Assume that air is \(21 \% \mathrm{O}_{2}\) and \(79 \% \mathrm{~N}_{2}\) by volume. If the barometric pressure is \(740 \mathrm{~mm}\), the partial pressure of \(\mathrm{O}_{2}\) is closest to which one of the following (a) \(155 \mathrm{~mm}\) (b) \(310 \mathrm{~mm}\) (c) \(580 \mathrm{~mm}\) (d) \(740 \mathrm{~mm}\)

Step-by-Step Solution

Answer

The partial pressure of O2 is closest to (a) 155 mm.

Step 1: Understand the concept of partial pressure

Partial pressure is the pressure that would be exerted by one of the gases in a mixture if it occupied the entire volume of the mixture by itself at the same temperature. The partial pressure of a gas in a mixture is determined by its fraction in the mixture and the total pressure.

Step 2: Calculate the partial pressure of O2

To find the partial pressure of O2, multiply the total pressure by the volume percentage of O2 in air. For O2, this is: \(740 \, \mathrm{mm} \times 0.21 \approx 155.4 \, \mathrm{mm}\).

Step 3: Match the result to the closest given option

Compare the calculated partial pressure of O2 to the given options and choose the closest one. Here, 155.4 mm is closest to option (a) 155 mm.

Key Concepts

Partial Pressure

Imagine you are at a party and there's a mix of several kinds of music playing at once. When you focus on one song, the others still contribute to the overall noise level. Similarly, in a gas mixture, each gas contributes a portion of the pressure like a song contributes to the overall sound. This portion is what we call the partial pressure.

It’s the pressure that one gas in a mixture would exert if it alone occupied the entire container. To calculate the partial pressure, you simply take the total pressure and multiply it by the percentage of the specific gas in the mixture. This is similar to turning up the volume on just one song and measuring how loud it is. Therefore, for oxygen, with a 21% presence in air, if the barometric (total) pressure is 740 mmHg, you multiply 740 by 0.21 to find its partial pressure.

Understanding partial pressure is crucial because it's foundational in fields like chemistry, environmental sciences, and medicine – for instance, when calculating how much oxygen is available for breathing at high altitudes or underwater. To enhance your comprehension, consider visual aids like diagrams of gas particles in a container, showing how each type contributes to the total pressure.

Gas Mixtures

Like a painter blending colors to get the perfect shade, nature blends gases to form the air we breathe. A gas mixture is simply two or more gases combined, like the mixture of oxygen and nitrogen that makes up our atmosphere.

Each gas in the mixture obeys the same physical laws as if it were alone. That's because gas particles are far apart and don't interact much with each other. This allows us to treat each gas independently when calculating properties like partial pressure. In our exercise, air consists of 21% oxygen and 79% nitrogen by volume. So when given the total pressure, you can calculate how much each gas contributes as if it was the only gas present.

For a clearer understanding, imagine a container with different colored balls representing various gases. Despite being mixed, you can count how many of each color there are for a percentage comparison. This helps visualize how each gas's proportion affects its partial pressure and therefore its behavior in the mixture.

Barometric Pressure

The weight of the atmosphere above us might feel like a lot to carry, but what we’re actually feeling is the barometric pressure. It's the force per unit area exerted by the Earth's atmosphere at any given point and is measured by an instrument called a barometer. This type of pressure changes with altitude and weather, affecting everything from our weather forecasts to our breathing.

Barometric pressure is like the baseline volume of all the songs playing at our metaphorical party, setting the overall loudness level. This full atmospheric pressure at sea level averages around 760 mmHg but can vary. The exercise's 740 mmHg can be understood as a slightly quieter day in terms of atmospheric loudness.

To tie it back to our earlier concepts, when you know the total atmospheric (barometric) pressure, you can determine the partial pressure of each gas in the mix. Using daily life examples, like the way we experience shifts in weather or the popping of our ears in an airplane, can make understanding barometric pressure more relatable and graspable.