If the quantity of oxygen occupying 2.76L container at a pressure of 0.825 atm and 300k is reduced by…

Analysis

To solve this problem, we need to understand the relationship between the amount of gas (moles) and the pressure it exerts within a fixed volume and temperature. This is governed by the Ideal Gas Law.

Concept

The Ideal Gas Law is expressed as:

Where:

• P = Pressure
• V = Volume
• n = Number of moles (quantity of gas)
• R = Universal gas constant
• T = Temperature

In this scenario, the volume ($V$), temperature ($T$), and the gas constant ($R$) remain constant. Therefore, the pressure ($P$) is directly proportional to the number of moles ($n$):

This means that if you change the quantity of gas ($n$) while keeping $V$ and $T$ constant, the pressure will change by the same factor.

Solution

1. Identify the initial state: • Initial Pressure ($P_1$) = 0.825 atm • Initial quantity ($n_1$) = $n$

2. Identify the final state: • The quantity of gas is reduced by one-half: $n_2 = \frac{1}{2}n_1$ • Since $P \propto n$, the new pressure ($P_2$) will also be one-half of the initial pressure.

3. Calculate the new pressure: $$P_2 = \frac{1}{2} \times P_1$$ $$P_2 = \frac{1}{2} \times 0.825 \text{ atm}$$ $$P_2 = 0.4125 \text{ atm}$$

Rounding to three decimal places as seen in the options, we get 0.413 atm.

Conclusion

Comparing our result to the given options, the correct value is 0.413 atm.

Exam Tip

Whenever you see a gas law problem, identify which variables are changing and which are held constant. If $V$ and $T$ are constant, you don't need to perform complex calculations with the Ideal Gas Law; simply look at how the change in moles ($n$) affects the pressure ($P$) directly!