How many molecules of O_2 occupy a volume of 1.0 L at 65 °C and 778 mm Hg? (Use R = 0.0821 L·atm·mol^{-1}·K^{-1} and 1 atm = 760 mm Hg.)

• A. 2.51 × 10^{23} molecules
• B. 3.12 × 10^{22} molecules
• C. 6.02 × 10^{23} molecules
• D. 1.98 × 10^{21} molecules

Answer: (B)

Verified step by step guidance

1. Convert the given pressure from mm Hg to atm using the conversion factor: \(P(\text{atm}) = \frac{P(\text{mm Hg})}{760}\).
2. Convert the temperature from Celsius to Kelvin using the formula: \(T(K) = T(^\circ C) + 273.15\).
3. Use the ideal gas law equation \(PV = nRT\) to solve for the number of moles \(n\) of \(O_2\). Rearrange the formula to: \(n = \frac{PV}{RT}\), where \(P\) is in atm, \(V\) is in liters, \(R\) is the gas constant, and \(T\) is in Kelvin.
4. Calculate the number of moles \(n\) by substituting the values of \(P\), \(V\), \(R\), and \(T\) into the rearranged ideal gas law equation.
5. Convert moles of \(O_2\) to molecules by multiplying the number of moles \(n\) by Avogadro's number \$6.022 \times 10^{23}$ molecules/mol.