Root mean square velocity of `O_2` at STP is (in `cm//s`)

Options

A. `4.61xx10^(4)`
B. `2.6xx10^(4)`
C. `46.1xx10^(4)`
D. `26.0xx10^(4)`

Answer

To find the root mean square velocity (VRMS) of oxygen (O2) at standard temperature and pressure (STP), we can follow these steps:

### Step 1: Understand the given parameters
At STP:
- Temperature (T) = 273 K
- The molecular mass of O2 = 32 g/mol (since O has a molar mass of 16 g/mol, and O2 has two oxygen atoms).

### Step 2: Use the formula for root mean square velocity
The formula for root mean square velocity is given by:

\[ V_{RMS} = \sqrt{\frac{3RT}{M}} \]

where:
- \( R \) is the universal gas constant = 8.314 J/(mol·K)
- \( T \) is the temperature in Kelvin
- \( M \) is the molar mass in kg/mol (we need to convert grams to kilograms).

### Step 3: Convert the molar mass to kg
Since the molar mass of O2 is 32 g/mol, we convert this to kg:

\[ M = \frac{32 \text{ g/mol}}{1000} = 0.032 \text{ kg/mol} \]

### Step 4: Substitute the values into the formula
Now substituting the values into the formula:

\[ V_{RMS} = \sqrt{\frac{3 \times 8.314 \text{ J/(mol·K)} \times 273 \text{ K}}{0.032 \text{ kg/mol}}} \]

### Step 5: Calculate the numerator
Calculating the numerator:

\[ 3 \times 8.314 \times 273 = 6818.622 \text{ J/mol} \]

### Step 6: Calculate the root mean square velocity
Now substituting this back into the equation:

\[ V_{RMS} = \sqrt{\frac{6818.622}{0.032}} = \sqrt{213,086.9375} \approx 462.8 \text{ m/s} \]

### Step 7: Convert to cm/s
To convert from m/s to cm/s, we multiply by 100:

\[ V_{RMS} \approx 462.8 \times 100 \approx 46280 \text{ cm/s} \]

### Final Answer
Thus, the root mean square velocity of O2 at STP is approximately **46280 cm/s**.