Question

Question: What is the bulk modulus of oxygen if 32.0 gmof oxygen occupies 22.4Land the speed of sound in the oxygen is 3.17 m/s?

Short answer

Answer

The bulk modulus of oxygen is $1.44\times {10}^5 Pa$.

Step-by-step solution

Given data

• The mass of the oxygen is m = 32.0gm .
• The volume of oxygen is

. $$\begin{gathered} V=22.4\text{L} \\ =0.0224{\text{m}}^{\text{3}} \end{gathered}$$

• The speed of the sound in oxygen gas is v = 317 m/s.

Determining the concept

By using the formulas for densityof oxygen gas and the speedof the sound in oxygen gas, find the bulk modulusof oxygen.

Formula is as follow:

The speed of the sound in oxygen gas is given by,

$v=\sqrt{\frac{B}{\rho }}$

Where, B is the bulk modulus of oxygen and$\rho$is the density of oxygen.

Determining the bulk modulus

The density “$\rho$”of oxygen gas is,

$\rho =\frac{m}{V}$

Substitute$0.0224{\text{m}}^{\text{3}}$ form ,$0.0224{\text{m}}^{\text{3}}$ for v into the above equation,

$$\begin{gathered} \rho =\frac{0.0320}{0.0224} \\ =1.43Kg/m^3 \end{gathered}$$

The speed of the sound in oxygen gas is given by,

$v=\sqrt{\frac{B}{\rho }}$

Here, B is the bulk modulus of oxygen and $\rho$is the density of oxygen.

Thus, the bulk modulus of oxygen is given by,

$B=\rho v^2$

Substitute$1.43Kg/m^3$for$\rho$ and 317 m/s for v into the above equation,

$$\begin{gathered} B=1.43\times {317}^2 \\ =1.44\times {10}^5 \text{Pa} \end{gathered}$$

Hence, the bulk modulus of oxygen is $1.44\times {10}^5 \text{Pa}$.