Find rms speed of Cobalt molecules at temperature `27^(@)C`.

Explanation

To find the root mean square (RMS) speed of cobalt molecules at a temperature of 27°C, we can follow these steps:

### Step-by-Step Solution:

1. **Convert the Temperature to Kelvin:**
The temperature given is 27°C. To convert this to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273.15 \]
Thus,
\[ T = 27 + 273.15 = 300.15 \approx 300 \, K \]

2. **Identify the Molar Mass of Cobalt:**
The molar mass of cobalt (Co) is approximately 59 g/mol. To use it in our calculations, we need to convert it to kilograms per mole:
\[ M = 59 \, g/mol = 59 \times 10^{-3} \, kg/mol \]

3. **Use the RMS Speed Formula:**
The formula for the RMS speed (\(v_{rms}\)) of a gas is given by:
\[ v_{rms} = \sqrt{\frac{3RT}{M}} \]
where:
- \(R\) is the gas constant, which is \(8.31 \, J/(K \cdot mol)\),
- \(T\) is the temperature in Kelvin,
- \(M\) is the molar mass in kg/mol.

4. **Substitute the Values into the Formula:**
Now, substituting the known values into the formula:
\[ v_{rms} = \sqrt{\frac{3 \times 8.31 \, J/(K \cdot mol) \times 300 \, K}{59 \times 10^{-3} \, kg/mol}} \]

5. **Calculate the RMS Speed:**
First, calculate the numerator:
\[ 3 \times 8.31 \times 300 = 7473 \, J/mol \]
Now, divide by the molar mass:
\[ \frac{7473}{59 \times 10^{-3}} = \frac{7473}{0.059} \approx 126,000 \, m^2/s^2 \]
Finally, take the square root:
\[ v_{rms} = \sqrt{126,000} \approx 356 \, m/s \]

### Final Answer:
The RMS speed of cobalt molecules at a temperature of 27°C is approximately **356 m/s**.