To find the molar mass of the gas, we can first use the Ideal Gas Law, which is represented by the formula:
\[ PV = nRT \]
Where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = number of moles of gas
- \( R \) = ideal gas constant
- \( T \) = temperature (in Kelvin)
We can rearrange this to find \( n \):
\[ n = \frac{PV}{RT} \]
Given:
- \( P = 0.95 \) atm
- \( V = 4.92 \) L
- \( R = 0.0821 , \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K} \)
- \( T = 280 , \text{K} \)
Plugging in the values:
\[ n = \frac{(0.95 , \text{atm})(4.92 , \text{L})}{(0.0821 , \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K})(280 , \text{K})} \]
Calculating the denominator:
\[ 0.0821 \cdot 280 = 22.996 , \text{L} \cdot \text{atm} / \text{mol} \]
Now plug in the values:
\[ n = \frac{(0.95)(4.92)}{22.996} \] \[ n = \frac{4.674}{22.996} \approx 0.203 , \text{mol} \]
Next, we need to find the molar mass (\( M \)) of the gas using the formula:
\[ M = \frac{\text{mass}}{n} \]
Given the mass of the gas is 5.49 g, we calculate:
\[ M = \frac{5.49 , \text{g}}{0.203 , \text{mol}} \approx 27.0 , \text{g/mol} \]
Thus, the molar mass of the gas is approximately 27 g/mol.