To find the molar mass of the gas, we can use the Ideal Gas Law equation, which is given by:
\[ PV = nRT \]
Where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = number of moles
- \( R \) = ideal gas constant (0.0821 L·atm/(mol·K))
- \( T \) = temperature (in Kelvin)
First, we need to calculate the number of moles \( n \) using the provided values:
Given:
- \( P = 0.95 , \text{atm} \)
- \( V = 4.92 , \text{L} \)
- \( R = 0.0821 , \text{L·atm/(mol·K)} \)
- \( T = 280 , \text{K} \)
We can rearrange the ideal gas law to solve for \( n \):
\[
n = \frac{PV}{RT}
\]
Substituting the known values:
\[
n = \frac{(0.95 , \text{atm})(4.92 , \text{L})}{(0.0821 , \text{L·atm/(mol·K)})(280 , \text{K})}
\]
Calculating the numerator:
\[
0.95 \times 4.92 = 4.674
\]
Calculating the denominator:
\[
0.0821 \times 280 = 22.988
\]
Now calculating \( n \):
\[
n = \frac{4.674}{22.988} \approx 0.203
\]
Now we have the number of moles. The molar mass \( M \) can be found using the formula:
\[
M = \frac{\text{mass}}{n}
\]
Given that the mass of the gas is 5.49 g:
\[
M = \frac{5.49 , \text{g}}{0.203 , \text{mol}} \approx 27.0 , \text{g/mol}
\]
Thus, the molar mass of the gas is approximately 27 g/mol.