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

Options

A. 548m/s
B. 483m/s
C. 254m/s
D. 148m/s

Explanation

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

### Step 1: Convert the temperature from Celsius to Kelvin
To convert the temperature from degrees Celsius to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273 \]
Given that the temperature is 27°C:
\[ T = 27 + 273 = 300 \, K \]

### Step 2: Identify the molecular weight of sulfur
The molecular weight of sulfur (S) is given as 32 g/mol. To use it in our calculations, we need to convert it to kilograms:
\[ m = 32 \, g/mol = 32 \times 10^{-3} \, kg/mol = 0.032 \, kg/mol \]

### Step 3: Use the rms speed formula
The formula for calculating the rms speed (\(v_{rms}\)) is:
\[ v_{rms} = \sqrt{\frac{3RT}{m}} \]
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

### Step 4: Substitute the values into the rms speed formula
Substituting the known values into the formula:
\[ v_{rms} = \sqrt{\frac{3 \times 8.31 \, J/(K \cdot mol) \times 300 \, K}{0.032 \, kg/mol}} \]

### Step 5: Calculate the value
First, calculate the numerator:
\[ 3 \times 8.31 \times 300 = 7479 \, J/mol \]
Now, divide by the molar mass:
\[ \frac{7479}{0.032} = 233715.625 \, m^2/s^2 \]
Now take the square root:
\[ v_{rms} = \sqrt{233715.625} \approx 483.44 \, m/s \]

### Step 6: Round the result
We can round the result to:
\[ v_{rms} \approx 483 \, m/s \]

### Final Answer
The rms speed of sulfur molecules at 27°C is approximately **483 m/s**.

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