What is the volume, in liters, of 15 moles of CO_2 gas at 50 °C and 800 torr? (Use R = 0.0821 L·atm·mol^{-1}·K^{-1})

• A. 460 L
• B. 580 L
• C. 570 L
• D. 720 L

Answer: (B)

Verified step by step guidance

1. Identify the known variables from the problem: number of moles \(n = 15\), temperature \(T = 50\ ^\circ\mathrm{C}\), pressure \(P = 800\ \mathrm{torr}\), and the gas constant \(R = 0.0821\ \mathrm{L \cdot atm \cdot mol^{-1} \cdot K^{-1}}\).
2. Convert the temperature from Celsius to Kelvin using the formula \(T(K) = T(^\circ C) + 273.15\). This is necessary because the ideal gas law requires temperature in Kelvin.
3. Convert the pressure from torr to atmospheres since the gas constant \(R\) is given in terms of atmospheres. Use the conversion \$1\ \mathrm{atm} = 760\ \mathrm{torr}\(, so \)P(\mathrm{atm}) = \frac{P(\mathrm{torr})}{760}$.
4. Use the ideal gas law equation \(PV = nRT\) to solve for the volume \(V\). Rearranged, the formula is \(V = \frac{nRT}{P}\).
5. Substitute the values of \(n\), \(R\), \(T\) (in Kelvin), and \(P\) (in atm) into the equation and solve for \(V\). This will give the volume in liters.