A sample of O_2 gas occupies 75 L at 2.0 atm and 300 K. What is the number of moles of O_2 present in the sample? (Use R = 0.0821 L·atm·mol^{-1}·K^{-1})

• A. 2.0 mol
• B. 3.7 mol
• C. 0.41 mol
• D. 6.1 mol

Answer: (D)

Verified step by step guidance

1. Identify the known variables from the problem: pressure \(P = 2.0\) atm, volume \(V = 75\) L, temperature \(T = 300\) K, and the gas constant \(R = 0.0821\) L\cdot atm\cdot mol^{-1}\cdot K^{-1}$.
2. Recall the Ideal Gas Law equation: \(P \times V = n \times R \times T\), where \(n\) is the number of moles of gas.
3. Rearrange the Ideal Gas Law to solve for \(n\): \(n = \frac{P \times V}{R \times T}\).
4. Substitute the known values into the rearranged equation: \(n = \frac{2.0 \times 75}{0.0821 \times 300}\).
5. Perform the arithmetic to calculate \(n\), which will give the number of moles of \(O_2\) in the sample.