To find the number of moles of gas in the container, you can use the Ideal Gas Law, which is expressed as:
\[ PV = nRT \]
Where:
- \( P \) = pressure in atmospheres (atm)
- \( V \) = volume in liters (L)
- \( n \) = number of moles (mol)
- \( R \) = ideal gas constant (\(0.0821 , \frac{L \cdot atm}{mol \cdot K}\))
- \( T \) = temperature in Kelvin (K)
Given:
- \( P = 2.00 , \text{atm} \)
- \( V = 3.00 , \text{L} \)
- \( T = 350 , \text{K} \)
Now, we can rearrange the Ideal Gas Law to solve for \( n \):
\[ n = \frac{PV}{RT} \]
Substituting the values into the equation:
\[ n = \frac{(2.00 , \text{atm}) (3.00 , \text{L})}{(0.0821 , \frac{L \cdot atm}{mol \cdot K})(350 , K)} \]
Calculating the numerator:
\[ 2.00 , \text{atm} \times 3.00 , \text{L} = 6.00 , \text{atm} \cdot \text{L} \]
Calculating the denominator:
\[ 0.0821 , \frac{L \cdot atm}{mol \cdot K} \times 350 , K = 28.735 , \frac{L \cdot atm}{mol} \]
Now, substitute the values into the equation for \( n \):
\[ n = \frac{6.00 , \text{atm} \cdot \text{L}}{28.735 , \frac{L \cdot atm}{mol}} \approx 0.209 , \text{mol} \]
Therefore, the number of moles of gas in the container is approximately \( 0.209 , \text{mol} \).