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At \(27^{\circ} \mathrm{C}\) a sample of ammonia gas exerts a pressure of \(5.3 \mathrm{~atm} .\) What is the pressure when the volume of the gas is reduced to one-tenth of the original value at the same temperature? (a) \(0.53\) atm (b) \(5.3 \mathrm{~atm}\) (c) \(53 \mathrm{~atm}\) (d) None of these

Short Answer

Expert verified
The pressure when the volume of the gas is reduced to one-tenth of the original value at the same temperature is 53 atm, which corresponds to option (c).

Step by step solution

01

Identify the relationship between pressure and volume

Since the temperature is constant, we can use Boyle's law which states that the pressure of a gas is inversely proportional to its volume. Mathematically, this is represented as P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
02

Set up the equation with known values

We know P1 is 5.3 atm and V2 is one-tenth of V1, so we can write the relationship as 5.3 atm * V1 = P2 * (V1/10).
03

Solve for P2

To isolate P2, multiply both sides of the equation by 10/V1. This simplifies to P2 = (5.3 atm * V1 * 10) / V1. The V1 terms cancel out, leaving P2 = 5.3 atm * 10.
04

Calculate the final pressure

The final step is to multiply 5.3 atm by 10, which gives P2 = 53 atm.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Gas Laws: Understanding the Basics
Gas laws are fundamental principles that describe the behavior of gases under various conditions of pressure, temperature, and volume. They are essential in the study of physical chemistry and thermodynamics and are frequently encountered in problems for exams like the JEE in Chemistry.

One of the most well-known gas laws is Boyle's Law. It specifically describes the pressure-volume relationship of a gas at a constant temperature. According to Boyle's Law, the pressure exerted by a gas is inversely proportional to its volume. This inverse relationship holds as long as the amount of gas and the temperature are held constant.

The significance of gas laws, especially in JEE Chemistry problems, cannot be overstated. They form the foundation for many applications in fields like environmental science, engineering, and even medicine. By understanding these laws, students can solve complex problems that involve predicting the behavior of gases under changing conditions.
Pressure-Volume Relationship: Boyle's Law in Action
The pressure-volume relationship is a key aspect of Boyle's Law, one of the fundamental gas laws in chemistry. It indicates that for a given amount of gas at a constant temperature, the pressure is inversely related to the volume. That means if the volume of a gas decreases, the pressure increases, assuming the temperature remains unchanged.

For instance, when you compress the air in a bicycle pump, its volume decreases but the pressure inside increases, which is why you feel more resistance as you continue to push down. This principle is applied in countless real-world applications such as in the workings of a syringe, hydraulic brakes, and even the human lungs during breathing.
JEE Chemistry Problems: Tackling Real-World Applications
JEE Chemistry problems often delve into real-world applications of scientific concepts such as those involving the behavior of gases. These problems are designed to test a student's conceptual understanding, analytical skills, and ability to apply theoretical knowledge to practical situations.

When encountering a JEE Chemistry problem that involves Boyle's Law, it’s important to carefully read the question, identify the constant parameters (as temperature in Boyle's Law problems), and then apply the appropriate formula. The formula for Boyle's Law, which is the core of many pressure-volume relationship questions, enables students to predict the outcome of changing pressure or volume conditions on a gas.
Physical Chemistry Exercises: Developing a Problem-Solving Mindset
Physical Chemistry exercises require a thorough understanding of the principles of chemistry and physics. They are designed to build a strong foundation in the mechanisms underlying chemical phenomena, particularly those related to changes in states and conditions of matter.

In practicing such exercises, it is crucial to adopt a problem-solving mindset. This involves visualizing the scenario, such as the compression of a gas, identifying the variables involved, and methodically applying the governing laws. Exercises revolving around Boyle's Law, for instance, will strengthen a student’s ability to work with the pressure-volume relationship, sharpening their analytical and mathematical skills in the process.
Thermodynamics: The Study of Energy and Work
Thermodynamics is a branch of physics that involves the study of energy, work, and heat and how they interplay with physical systems. In the context of gas laws, thermodynamics explores how energy is transferred in the form of work during the compression or expansion of gases.

Boyle's Law, while primarily concerned with the pressure-volume relationship at a constant temperature, is inherently connected to thermodynamics as work is done when the volume of the gas changes. Understanding how work and heat transfer affects the behavior of gases is crucial for applications ranging from internal combustion engines to refrigeration cycles, making thermodynamics a vital area of study for students tackling comprehensive chemistry problems.

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Most popular questions from this chapter

A certain sample of gas has a volume of \(0.2\) litre measured at 1 atm pressure and \(0^{\circ} \mathrm{C}\). At the same pressure but at \(273^{\circ} \mathrm{C}\), its volume will be: (a) \(0.4\) litre (b) \(0.8\) litre (c) \(27.8\) litres (d) \(55.6\) litres

Under identical conditions of pressure and temperature, \(4 \mathrm{~L}\) of gaseous mixture \(\left(\mathrm{H}_{2}\right.\) and \(\left.\mathrm{CH}_{4}\right)\) effuses through a hole in 5 min whereas \(4 \mathrm{~L}\) of a gas \(X\) of molecular mass 36 takes to \(10 \mathrm{~min}\) to effuse through the same hole. The mole ratio of \(\mathrm{H}_{2}: \mathrm{CH}_{4}\) in the mixture is : (a) \(1: 2\) (b) \(2: 1\) (c) \(2: 3\) (d) \(1: 1\)

Select the correct statement : (a) internal energy of a real gas at a given temperature increases as the volume increases (b) internal energy of an ideal gas at given temperature increase as the volume increases (c) internal energy of an ideal gas molecules is not a function of temperature (d) the internal energy of a real gas at a constant temperature is independent of change in volume

Densities of two gases are in the ratio \(1: 2\) and their temperatures are in the ratio \(2: 1\), then the ratio of their respective molar mass at certain pressure is: (a) \(1: 1\) (b) \(1: 2\) (c) \(2: 1\) (d) \(4: 1\)

At identical temperature and pressure, the rate of diffusion of hydrogen.gas is \(3 \sqrt{3}\) times that of a hydrocarbon having molecular formula \(\mathrm{C}_{n} \mathrm{H}_{2 n-2}\). What is the value of \(n\) ? (a) 1 (b) 4 (c) 3 (d) 8

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