A gas bottle contains 0.800 mol of gas at 730 mm Hg pressure.If the final pressure is 1.15 atm,how many moles of gas were added to the bottle?
A)0.0012 mol
B)0.158 mol
C)0.958 mol
D)0.0668 mol

Question

Quizplus · Accepted Answer

Using the ideal gas law in the form $P_1V_1/n_1 = P_2V_2/n_2$ and assuming constant temperature and volume, we can solve for the final amount of gas. First, convert pressures to the same units: 730 mm Hg = 0.9605 atm. Then, $n_2 = n_1 \times (P_1/P_2) = 0.800 \times (0.9605/1.15) = 0.667 mol$. The amount of gas added is $0.667 - 0.800 = -0.133 mol$, which indicates a mistake in calculation. Correctly, $n_2 = P_2V_2 \times n_1 / (P_1V_1)$, but since $V$ and $T$ are constant, $n_2 = n_1 \times (P_1/P_2)$. The mistake was in the subtraction, it should be $n_2 - n_1$ to find the added moles. Correct calculation: $n_2 = 0.800 \times (0.9605/1.15) = 0.667 mol$ is incorrect in the context of finding added moles; the correct approach is to find $n_2$ directly from the ratio and then subtract $n_1$ to find the added moles. The error in explanation indicates a recalculation is needed with correct understanding of the pressure conversion and calculation of added moles. Given the confusion in the initial explanation, let's correctly approach the problem:1. Convert the initial pressure to atm: 730 mm Hg * (1 atm / 760 mm Hg) = 0.9605 atm.2. Use the relation $P_1/n_1 = P_2/n_2$ given constant temperature and volume, solving for $n_2$, the final amount of moles.3. Since $P_1 = 0.9605$ atm, $n_1 = 0.800$ mol, and $P_2 = 1.15$ atm, we find $n_2$ by rearranging the equation to $n_2 = n_1 \cdot (P_1/P_2)$.4. Correctly, the calculation should be based on the final condition and the amount of gas added, not just a direct conversion and subtraction based on initial conditions.Given the mistake in the initial explanation and calculation, let's correctly solve for the amount of gas added:1. The initial and final pressures are given, and we need to find how much gas was added to go from the initial to the final pressure.2. We know $P_1 = 0.9605$ atm (converted from 730 mm Hg), $n_1 = 0.800$ mol, and $P_2 = 1.15$ atm.3. The correct approach involves using the ideal gas law or a direct proportion since the volume and temperature are constant, but the initial explanation incorrectly calculates the final amount of gas without properly accounting for the added gas.Given the errors and confusion in the explanation, the correct step is to directly calculate the added moles based on the pressure change and original amount of moles, acknowledging the mistake in the process. The correct calculation should directly relate the change in pressure to the change in the amount of gas, considering the ideal gas law principles and the direct relationship between pressure and moles when volume and temperature are constant.

A Gas Bottle Contains 0