Question

Ideal gas equation is also called equation of states because (a) it depends on states of matter (b) it is a relation between four variables and describes the state of any gas (c) it is combination of various gas laws and any variable can be calculated (d) it is applicable to only ideal gases under STP conditions.

Short answer

The ideal gas equation is called an equation of state because (b) it is a relation between four variables and describes the state of any gas.

Step-by-step solution

Understanding the Definition of an Equation of State

An equation of state is a mathematical model that describes the state of matter under a given set of physical conditions. It typically relates variables such as pressure, volume, temperature, and amount of substance.

Analyzing Options

We need to consider each option and analyze it against the definition of an equation of state:(a) It's not enough for the equation to simply depend on the states of matter, it must relate specific properties of those states.(b) Yes, the ideal gas equation relates four variables (pressure, volume, temperature, amount of substance) and can describe the state of a gas.(c) While the ideal gas law is a combination of various gas laws, this doesn't necessarily qualify it as an equation of state.(d) The ideal gas law is not strictly limited to STP conditions and it's an approximation for actual gases under a range of conditions, not just ideal gases at STP.

Selecting the Correct Option

Based on the analysis, the most appropriate reason that the ideal gas equation is called an equation of state is because it relates the four variables defining the state of any gas. Therefore, option (b) is the correct answer.

Key concepts

Equation of State

When we talk about an equation of state, we refer to a mathematical relationship that seamlessly connects the different physical properties of a substance. In the realm of gases, this equation is unique because it captures the essence of a gas's behavior under a wide variety of conditions.

The ideal gas equation, which is \( PV = nRT \) where P stands for pressure, V for volume, n for the number of moles of the gas, R is the universal gas constant, and T is the temperature in Kelvin, serves as a classic example of such an equation. This relationship helps us predict how a gas will react when we change the pressure, volume, or temperature - making it an indispensable tool for scientists and engineers.

Physical Conditions of Matter

Matter exists in various states such as solid, liquid, and gas, each with its own unique characteristics. The physical conditions that define these states include pressure, volume, and temperature. These properties are not just numbers; they tell a story about how particles within the matter interact with each other.

For instance, in a gas, the particles are far apart and move freely, while in a solid they are closely packed and vibrate in place. The ideal gas law is particularly centered around gases, as it implies that the gas particles are in random motion and do not interact with one another, an assumption that holds true for an ideal gas but may slightly deviate in real gases.

Pressure, Volume, Temperature Relationship

Understanding the interplay between pressure, volume, and temperature is key to grasping how gases behave. Pressure is the force a gas exerts per unit area, volume is the amount of space it occupies, and temperature is a measure of the average kinetic energy of its particles.

The ideal gas law shows that if you hold one of these variables constant, changing another will affect the third. For example, increasing the temperature while keeping volume constant will increase pressure, a principle that explains phenomena like the expansion of car tires on a hot day.