Chapter 13.2, Problem 1RQ

Interpretation Introduction

Interpretation:

The ideal gas law have to be described.

Concept Introduction:

The ideal gas law was derived by combining three important laws of the gases.

Boyle’s law: $V\propto \frac{1}{P}$ When T is constant

Charles’s law: $V\propto \mathrm{T}$ When P is constant

Avogadro’s law: $V\propto n$ When P and T are constant

The ideal gas law can be expressed as-

  $\begin{array}{l}V\propto \frac{\mathrm{n}T}{P}\\ \mathrm{PV}=nRT\end{array}$ Where, R is universal gas constant.

The ideal gas law consists of all the variables of a gas such as pressure (P), volume (V), number of moles (n) and temperature (T).

Answer to Problem 1RQ

Keeping the variables that change are on one side and all constant variables to the other side of the equation. We can get an equation consists of the variables that are changing with initial and final state. The initial variables in one the side is equal to the final variables with the other side of the final equation. By solving the equation the missing variable can be obtained.

Explanation of Solution

The ideal gas law consists of all the variables of a gas such as pressure (P), volume (V), number of moles (n) and temperature (T).

  $\mathrm{PV}=nRT$

The ideal gas equation can be written in such a way that the variables that change are on one side and the constant variables are on the other side. Keeping both n and T constant and varies P and V, the ideal gas equation can be written as-

  $\mathrm{PV}=nRT$ Where ‘nRT’ is constant while P and V are changing.

So, we can write P₁V₁ = nRT and P₂V₂ = nRT.

Combining these gives

  ${\mathrm{P}}_1{V}_1=P_2{V}_2$ This is an expression of Boyle’s law.

So by keeping n and T constant, the Boyle’s law equation is obtained from the ideal gas equation. All types of gas law problems can be solved by the ideal gas equation using this idea.