To find the molar mass of the gas, we can use the ideal gas law equation:
\[ PV = nRT \]
where:
- \( P \) is the pressure (in atm)
- \( V \) is the volume (in liters)
- \( n \) is the number of moles
- \( R \) is the ideal gas constant (\(0.0821 , \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K}\))
- \( T \) is the temperature (in Kelvin)
First, let's calculate the number of moles (\( n \)) of the gas using the given conditions:
- \( P = 0.95 , \text{atm} \)
- \( V = 4.92 , \text{L} \)
- \( T = 280 , \text{K} \)
We rearrange the ideal gas law to solve for \( n \):
\[ n = \frac{PV}{RT} \]
Substituting in the values we have:
\[ n = \frac{(0.95 , \text{atm}) (4.92 , \text{L})}{(0.0821 , \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K}) (280 , \text{K})} \]
Calculating the right-hand side:
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Calculate the numerator: \[ 0.95 \times 4.92 = 4.674 \]
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Calculate the denominator: \[ 0.0821 \times 280 = 22.988 \]
Now, substituting these values into the equation for \( n \):
\[ n = \frac{4.674}{22.988} \approx 0.203 , \text{mol} \]
Now we can find the molar mass (\( M \)) of the gas using the formula:
\[ M = \frac{\text{mass}}{n} \]
We know that the mass of the gas is 5.49 g, so we can calculate the molar mass:
\[ M = \frac{5.49 , \text{g}}{0.203 , \text{mol}} \approx 27.0 , \text{g/mol} \]
Therefore, the molar mass of the gas is approximately 27 g/mol.
The correct answer is 27 g/mol.