Determine the pressure of nitrogen at `0 ""^(@)C` if the density of nitrogen at N.T.P. is 1.25 `kg//m^(3)` and R.M.S. speed of the molecules at N.T.P. is 489 m/s.

Answer

To determine the pressure of nitrogen at 0 °C using the given information, we can use the formula that relates pressure (P) to density (ρ) and the root mean square (RMS) speed (V) of the gas molecules:

\[ P = \frac{1}{3} \rho V^2 \]

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Density of nitrogen (ρ) = 1.25 kg/m³
- RMS speed of nitrogen molecules (V) = 489 m/s

2. **Substitute the Values into the Formula:**
\[ P = \frac{1}{3} \times 1.25 \, \text{kg/m}^3 \times (489 \, \text{m/s})^2 \]

3. **Calculate \( V^2 \):**
\[ V^2 = 489^2 = 239121 \, \text{m}^2/\text{s}^2 \]

4. **Multiply by Density:**
\[ \rho V^2 = 1.25 \times 239121 = 298901.25 \, \text{kg/(m s}^2\text{)} = 298901.25 \, \text{N/m}^2 \]

5. **Calculate Pressure:**
\[ P = \frac{1}{3} \times 298901.25 = 99633.75 \, \text{N/m}^2 \]

6. **Convert to Pascal:**
\[ P = 99633.75 \, \text{Pa} \]

### Final Answer:
The pressure of nitrogen at 0 °C is approximately **99633.75 Pa**.