Question

A \(2.24 \mathrm{~L}\) cylinder of oxygen at \(1 \mathrm{~atm}\) and \(273 \mathrm{~K}\) is found to develop a leakage. When the leakage was plugged the pressure dropped to \(570 \mathrm{~mm}\) of \(\mathrm{Hg}\). The number of moles of gas that escaped will be : (a) \(0.025\) (b) \(0.050\) (c) \(0.075\) (d) \(0.09\)

Short answer

0.025 moles of gas escaped.

Step-by-step solution

Convert pressure from mm Hg to atm

First, convert the pressure after the leakage from millimeters of mercury to atmospheres, because the initial conditions were given in atmospheres. The conversion factor is 1 atm = 760 mm Hg.

Use the Ideal Gas Law to find the initial number of moles

Use the Ideal Gas Law equation, PV=nRT, with the initial conditions to calculate the initial number of moles (n_initial) of oxygen. Use the value of R as 0.0821 L atm/(mol K).

Use the Ideal Gas Law to find the final number of moles

Apply the Ideal Gas Law again with the final conditions (after the leakage) to determine the number of moles left (n_final). It's important to use the pressure converted to atmospheres in this step.

Calculate the number of moles that escaped

Find the difference between the initial and final number of moles to determine the number of moles that escaped: n_escaped = n_initial - n_final.

Choose the correct answer

Finally, match the calculated moles of gas that escaped with the given options to find the correct answer.

Key concepts

Chemical Problem Solving

Tackling chemical problems effectively begins with a clear understanding of the given data, the required solution, and the principles that bridge the two. This process is particularly vital when dealing with exercises that involve the Ideal Gas Law, a fundamental component in many chemistry problems. The first step in chemical problem solving usually involves unit conversions to ensure consistency, as illustrated in the textbook exercise where you convert pressure from mm Hg to atm. Such conversions are crucial because they align the units across all measured variables, allowing the use of equations like the Ideal Gas Law.

Next is interpreting and applying the correct chemical principle or formula. The Ideal Gas Law, written as \( PV=nRT \), where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature, serves as a powerful tool in this regard. By plugging in known values and solving for the unknown, you can navigate through the problem. However, chemical problem solving does not end at finding the numerical answer; verifying this answer against given choices is just as important. It ensures your solution is not just calculated correctly but is also conceptually sound.

Gas Laws in Chemistry

The Gas Laws in chemistry are a collection of rules governing the behavior of gases under various conditions. The Ideal Gas Law is one of the foundational pillars of this group and helps predict how a gas will change under different temperature, volume, and pressure scenarios. One key application is determining the amount of gas in a system, as in our original problem.

Understanding the use of the Ideal Gas Law involves more than just memorizing the equation; it requires comprehension of how each variable interrelates. For example, if a gas expands, the pressure decreases if the temperature is constant, according to Boyle's Law, one of the specific gas laws that are integrated into the Ideal Gas Law. Similarly, Charles's Law states that with constant pressure, the volume of a gas increases as the temperature increases. This concrete understanding of how the variables affect one another will help you not only solve textbook problems but also apply these concepts practically, in areas such as predicting the behavior of gases in real-life situations or industrial processes.

JEE Chemistry Preparation

Preparing for competitive exams like the Joint Entrance Examination (JEE) in Chemistry involves a deep dive into concepts, practicing a variety of problems, and developing test-taking strategies. In the context of our exercise involving the Ideal Gas Law, such preparation would include mastering the various gas laws, understanding their real-world applications, and practicing conversion between different units, a skill that is often tested.

Additional preparation should focus on speed and accuracy, given the time constraints of the exam. Conceptual clarity is achieved by solving a wide array of problems, from basics to advanced applications of the gas laws, ensuring that problems on the Ideal Gas Law or related concepts can be approached with confidence. Optimal JEE Chemistry preparation blends rigorous practice with clear conceptual understanding and efficient problem-solving strategies such as the elimination of incorrect options, an approach that can save valuable time during the actual exam.