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