Question

"Equal volumes of all gases at the same temperature and pressure contain equal number of particles." This statement is a direct consequence of : (a) Avogadro's law (b) Charle's law (c) Ideal gas equation (d) Law of partial pressure

Short answer

The statement is a direct consequence of Avogadro's law (a).

Step-by-step solution

Understanding the Statement

The given statement, 'Equal volumes of all gases at the same temperature and pressure contain equal number of particles,' implies a direct relationship between the volume of a gas and the number of particles it contains, given that temperature and pressure are held constant.

Identifying the Relevant Gas Law

To find out which gas law the statement is a direct consequence of, review the main aspects of each choice: (a) Avogadro's law - directly relates the volume of a gas to the number of particles at constant temperature and pressure; (b) Charles's law - relates the volume of a gas to its temperature at constant pressure; (c) Ideal gas equation - relates the pressure, volume, temperature, and number of particles of a gas; (d) Law of partial pressures - concerns the pressure exerted by individual gas components in a mixture.

Arriving at the Correct Law

Since the statement focuses on the relationship of volume and number of particles while temperature and pressure are constant, it aligns with Avogadro's law. This law states that equal volumes of gases, at the same temperature and pressure, have the same number of particles.

Key concepts

Ideal Gas Equation

The ideal gas equation is a foundational concept in chemistry that relates the pressure (P), volume (V), temperature (T), and number of particles (n) of a gas. Represented as \(PV = nRT\), where R is the universal gas constant, this equation is central to understanding the behavior of gases under different conditions. The ideal gas law assumes that the gas particles do not interact and that the volume of the gas particles is negligible compared to the volume of the container.

For students grappling with gas problems, the ideal gas equation can be thought of as an extension of Avogadro's, Charles's, and Boyle’s laws. It embodies the principles that these individual laws describe, providing a comprehensive equation that can be used to calculate any one of the variables if the other three are known. This is particularly useful when dealing with exercises that require manipulation of more than one gas law, offering a unified approach to solve complex scenarios.

Charles's Law

Charles's law is a principle that describes how gases tend to expand when heated. In a more scientific language, it states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature (in Kelvin). This can be expressed mathematically as \( \frac{V1}{T1} = \frac{V2}{T2} \), where V refers to volume and T to temperature. This means that if you increase the temperature of a gas, its volume will also increase if the pressure is kept the same, and vice versa.

When it comes to understanding textbook exercises, remembering that Charles's law is about temperature and volume can greatly simplify deciphering problems. For instance, if an exercise asks you what happens to the volume of a gas when the temperature is doubled, Charles's law provides the answer: the volume also doubles, as long as pressure remains unchanged. This law is particularly helpful for explaining phenomena like hot air balloons rising when heated.

Law of Partial Pressure

The law of partial pressure, also known as Dalton's law, is crucial for understanding the behavior of gas mixtures. It states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases present in the mixture. The partial pressure of each gas is the pressure that the gas would exert if it alone occupied the total volume of the mixture at the same temperature. This law can be expressed as \(P_{total} = P_1 + P_2 + P_3 + ... + P_n\), where each \(P\) represents the partial pressure of each gas.

Students can leverage this law when solving exercises involving gas mixtures. For example, if you know the individual partial pressures and need to find the total pressure, simply add them up. Conversely, if you know the total pressure and the percentage composition of the mixture, you can calculate the partial pressure of each component. This law is used in a wide range of applications, including respiratory gas analysis and the calculation of reactants and products in chemical reactions.