Calculate the root mean square speed of hydrogen molecules at `373.15 K`.

Explanation

To calculate the root mean square speed of hydrogen molecules at a temperature of 373.15 K, we can follow these steps:

### Step 1: Identify the given values
- Temperature (T) = 373.15 K
- Molar mass of hydrogen (M) = 2 g/mol = 2 x 10^-3 kg/mol
- Universal gas constant (R) = 8.31 J/(mol·K)

### Step 2: Write the formula for root mean square speed
The formula for the root mean square speed (Vrms) of gas molecules is given by:
\[ V_{rms} = \sqrt{\frac{3RT}{M}} \]

### Step 3: Substitute the values into the formula
Now, we substitute the known values into the formula:
\[ V_{rms} = \sqrt{\frac{3 \times 8.31 \, \text{J/(mol·K)} \times 373.15 \, \text{K}}{2 \times 10^{-3} \, \text{kg/mol}}} \]

### Step 4: Calculate the numerator
First, calculate the numerator:
\[ 3 \times 8.31 \times 373.15 = 3 \times 8.31 \times 373.15 \approx 9318.36 \, \text{J/mol} \]

### Step 5: Calculate the entire expression
Now, divide the result by the molar mass:
\[ \frac{9318.36 \, \text{J/mol}}{2 \times 10^{-3} \, \text{kg/mol}} = \frac{9318.36}{0.002} \approx 4659180 \, \text{m}^2/\text{s}^2 \]

### Step 6: Take the square root
Now, take the square root of the result:
\[ V_{rms} = \sqrt{4659180} \approx 2157.14 \, \text{m/s} \]

### Step 7: Final Result
Thus, the root mean square speed of hydrogen molecules at 373.15 K is approximately:
\[ V_{rms} \approx 2156 \, \text{m/s} \quad \text{or} \quad 2.16 \, \text{km/s} \]