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Gases have a characteristic property known as density, which tells us how much mass is contained in a given volume. It is calculated using the formula \[ \text{Density (} \rho \text{)} = \frac{\text{mass}}{\text{volume}} \]where mass is usually in grams (g) and volume in liters (L). This calculation shows how tightly packed the molecules in a gas are. For example, in the case of oxygen in our exercise, we have 32.0 g of the gas occupying 22.4 L.

• This leads to a density of \( \rho = \frac{32.0}{22.4} \) g/L.

For calculations in physics, density is often converted to standard international (SI) units, like kg/m³. Knowing the conversion is straightforward:

• 1 g/L is equivalent to 1 kg/m³.

This makes computations easier, especially when linked with other SI units in formulas, such as the bulk modulus.

The speed of sound in a medium, like a gas, reflects how quickly sound waves pass through it. This speed is a crucial parameter in determining the medium's bulk modulus. The speed of sound relies on variables such as the medium's density and its elastic properties.

• In the case of oxygen, the speed of sound is given as 317 m/s.

The formula that ties speed of sound \( v \) with density \( \rho \) in determining the bulk modulus \( B \) is:\[ B = \rho v^2 \]This equation shows that as the speed of sound increases, so does the bulk modulus. In simple terms, a higher speed of sound indicates a stiffer medium that resists compression more.

Uniform compression describes how a substance reacts evenly to applied pressure or compression across all directions. It is a core concept in understanding the bulk modulus, which quantifies this reaction. In our exercise, the bulk modulus calculation shows how resistant oxygen is to being uniformly compressed. When we know both the density and the speed of sound in the gas, the bulk modulus provides insight into this resistance.

• A large bulk modulus value indicates high resistance to compression.

So, the bulk modulus \( B \) calculated, such as 143741.4 N/m² for oxygen here, translates to the gas's strong resistance to being compressed uniformly throughout its volume. This numerical value is crucial for various applications, including understanding sound propagation and acoustic properties through gases.