Calculate the rms velocity of oxygen at STP, density of oxygen is 1.44 `kgm^(-3)`

Explanation

To calculate the root mean square (rms) velocity of oxygen at standard temperature and pressure (STP), we can follow these steps:

### Step 1: Identify the given values
- Density of oxygen (ρ) = 1.44 kg/m³
- Pressure at STP (P) = 1.013 × 10^5 Pa

### Step 2: Write the formula for rms velocity
The formula for the rms velocity (v_rms) is given by:
\[ v_{rms} = \sqrt{\frac{3P}{\rho}} \]
where P is the pressure and ρ is the density.

### Step 3: Substitute the known values into the formula
Now, we can substitute the values of P and ρ into the formula:
\[ v_{rms} = \sqrt{\frac{3 \times (1.013 \times 10^5)}{1.44}} \]

### Step 4: Calculate the numerator
First, calculate the numerator:
\[ 3 \times (1.013 \times 10^5) = 3.039 \times 10^5 \]

### Step 5: Divide by the density
Now, divide this result by the density:
\[ \frac{3.039 \times 10^5}{1.44} \approx 2.1104 \times 10^5 \]

### Step 6: Take the square root
Now, take the square root of the result:
\[ v_{rms} = \sqrt{2.1104 \times 10^5} \approx 459.3 \text{ m/s} \]

### Step 7: Final answer
Thus, the rms velocity of oxygen at STP is approximately:
\[ v_{rms} \approx 4.59 \times 10^2 \text{ m/s} \]

### Summary
The rms velocity of oxygen at STP is approximately 459.3 m/s.

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