Question

At what pressure a quantity of gas will occupy a volume of \(60 \mathrm{~mL}\), if it occupies a volume of \(100 \mathrm{~mL}\) at a pressure of \(720 \mathrm{~mm}\) (while temperature is constant): (a) \(700 \mathrm{~mm}\) (b) \(800 \mathrm{~mm}\) (c) \(100 \mathrm{~mm}\) (d) \(1200 \mathrm{~mm}\)

Short answer

The pressure at which the quantity of gas will occupy a volume of 60 mL is 1200 mm.

Step-by-step solution

Understand the relationship between pressure and volume

Since the temperature is constant, we can use Boyle's Law for this problem, which states that the pressure and volume of a gas have an inverse relationship when temperature is held constant. Mathematically, this can be expressed as P1 * V1 = P2 * V2, where P1 and V1 are the original pressure and volume, and P2 and V2 are the final pressure and volume.

Set up the equation using Boyle's Law

We'll insert the given values into Boyle's Law equation: P1 = 720 mm, V1 = 100 mL, V2 = 60 mL. We need to solve for P2.

Rearrange the equation to solve for P2

Rearrange the equation to isolate P2 on one side: P2 = (P1 * V1) / V2.

Calculate the new pressure P2

Using P1 = 720 mm and V1 = 100 mL, and V2 = 60 mL, we substitute these into the equation to get P2 = (720 mm * 100 mL) / 60 mL.

Simplify and compute the value of P2

Perform the calculation: P2 = (720 mm * 100 mL) / 60 mL = 72,000 mm*mL / 60 mL = 1200 mm. This is the final pressure when the gas occupies a volume of 60 mL at constant temperature.

Key concepts

Chemical Pressure-Volume Relationship

Understanding the relationship between pressure and volume of gases is an essential concept in chemical studies, particularly when examining how gases behave under varying conditions. The pressure-volume relationship is commonly referred to as Boyle's Law in chemistry. This law is particularly useful when dealing with chemical reactions and processes that involve gases at a constant temperature.

Boyle's Law states that for a given mass of gas at constant temperature, the pressure exerted by the gas is inversely proportional to its volume. In simple terms, this means that if you compress a gas, its pressure increases if the temperature remains the same, and conversely, if you expand a gas, its pressure decreases. This principle is fundamental when predicting how a gas will react to changes in volume, which is crucial in designing and understanding many types of chemical equipment and processes.

When applying Boyle's Law to solve problems, it's common to use the formula: \( P_1 \times V_1 = P_2 \times V_2 \), where \(P_1\) and \(V_1\) represent the initial pressure and volume, and \(P_2\) and \(V_2\) represent the final pressure and volume, respectively. The product of pressure and volume for any state of the gas must remain constant, enabling us to solve for unknown variables when other values are known.

JEE Chemistry

JEE Chemistry is a subsection of the Joint Entrance Examination (JEE), which is a highly competitive examination for aspiring engineers in India. It is a critical screening test for entry into prestigious engineering colleges, including the Indian Institutes of Technology (IITs). The chemistry section of JEE tests a student's understanding of physical, organic, and inorganic chemistry.

Boyle's Law and other gas laws are essential parts of the physical chemistry syllabus for JEE Chemistry. Students are tested on their conceptual understanding and their ability to solve practical problems related to pressure-volume relationships in gases. Mastering these concepts is crucial not only for high scores in competitive exams but also for pursuing a successful career in various fields of engineering and technology that involve chemical processes.

A strong grasp of Boyle's Law is important as it often forms the basis for more complex calculations involving gas mixtures, reactions under non-standard conditions, and even thermodynamic considerations. JEE aspirants should not only memorize the law but also practice applying it to various problems to solidify their understanding and increase their speed and accuracy during the exam.

Physical Chemistry

Physical chemistry is the branch that bridges the gap between physics and chemistry, dealing with the physical structure of chemicals and the energetic changes that accompany chemical processes. Within this field, the behavior of gases is a topic of paramount importance, and Boyle's Law is one of the fundamental principles that govern this behavior.

In physical chemistry, understanding how properties such as pressure, volume, and temperature interact is critical for predicting and manipulating chemical reactions and processes. Boyle's Law is frequently used alongside Charles's Law and Gay-Lussac's Law, and collectively these laws form the Combined Gas Law, which is a more general equation used to predict the state of a gas when it undergoes changes in pressure, volume, and temperature.

Knowledge of this law is not only theoretical but also practical. It is applied in creating and interpreting graphs that represent the pressure-volume relationship, which are used in multiple applications spanning from chemical engineering to environmental science. By manipulating the variables in the equation \( P_1 \times V_1 = P_2 \times V_2 \), chemists can predict outcomes in real-world scenarios, such as the expansion of gases in a closed container or the requirements for gas storage facilities.