What volume (in liters) is occupied by 500 g of fluorine gas (F_2) at 5.00 °C and a pressure of 735 torr? (Use R = 0.0821 L·atm·mol^{-1}·K^{-1})

• A. 154 L
• B. 112 L
• C. 98.6 L
• D. 210 L

Answer: (A)

Verified step by step guidance

1. Convert the given temperature from Celsius to Kelvin using the formula: \(T(K) = T(^\circ C) + 273.15\). For 5.00 °C, calculate \(T = 5.00 + 273.15\) K.
2. Convert the pressure from torr to atm because the gas constant R is given in atm. Use the conversion factor: \$1\ \text{atm} = 760\ \text{torr}\(. Calculate \)P(\text{atm}) = \frac{735}{760}$ atm.
3. Calculate the number of moles of fluorine gas (F\(_2\)) using its molar mass. The molar mass of F\(_2\) is approximately \$2 \times 18.998\( g/mol. Use the formula: \)n = \frac{\text{mass}}{\text{molar mass}} = \frac{500}{\text{molar mass}}$ mol.
4. Use the ideal gas law equation \(PV = nRT\) to solve for the volume \(V\). Rearrange the equation to \(V = \frac{nRT}{P}\), where \(P\) is in atm, \(n\) is moles, \(R = 0.0821\ \text{L}\cdot\text{atm}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}\), and \(T\) is in Kelvin.
5. Substitute the values of \(n\), \(R\), \(T\), and \(P\) into the equation and solve for \(V\) to find the volume occupied by the fluorine gas under the given conditions.