A gas bottle initially contains 0.800 mol of gas at a pressure of 730 mm Hg. If the final pressure is increased to 1.15 atm, how many moles of gas were added to the bottle, assuming constant temperature and volume?

• A. 0.800 mol
• B. 0.200 mol
• C. 0.600 mol
• D. 0.400 mol

Answer: (B)

Verified step by step guidance

1. Identify the initial and final conditions of the gas. Initially, the gas bottle contains 0.800 mol of gas at a pressure of 730 mm Hg. The final pressure is 1.15 atm. The temperature and volume are constant.
2. Convert the initial pressure from mm Hg to atm to ensure consistent units. Use the conversion factor: 1 atm = 760 mm Hg. Therefore, the initial pressure in atm is calculated as \( \frac{730 \text{ mm Hg}}{760 \text{ mm Hg/atm}} \).
3. Apply the ideal gas law in the form of \( P_1 \cdot n_1 = P_2 \cdot n_2 \), where \( P_1 \) and \( n_1 \) are the initial pressure and moles, and \( P_2 \) and \( n_2 \) are the final pressure and moles. Substitute the known values: \( P_1 = \frac{730}{760} \text{ atm} \), \( n_1 = 0.800 \text{ mol} \), and \( P_2 = 1.15 \text{ atm} \).
4. Rearrange the equation to solve for \( n_2 \), the final number of moles: \( n_2 = \frac{P_1 \cdot n_1}{P_2} \). Substitute the values to find \( n_2 \).
5. Calculate the number of moles added by subtracting the initial moles from the final moles: \( \text{moles added} = n_2 - n_1 \).