Question

How would the graph in Figure 9.12 change if the number of moles of gas in the sample used to determine the curve were doubled?

Short answer

The line steepens twice as much.

Step-by-step solution

Defining a mole

A mole is used to describe an amount that cannot be quantified in grams or milligrams. So, a mole is a unit of measurement for a number of atoms, ions, or molecules.

Explanation

Charles' law is depicted in a different way in this diagram.

Statement of Charles’ law:

Given a certain quantity of gas and a fixed pressure, the ratio between temperature in kelvin and volume is constant.

\begin{aligned} {\frac{V}{T}}=\texttt{constant}\end{aligned}

Figure 9.12 shows a graph

The graph depicts the volume versus the temperature of 1 mole of gas at 1 bar of pressure as an example of Charles’ law.

In accordance with Charles’ law in a rearranged form, V = const×T, const being the slope of the line on the graph. The resultant curve is linear (y = ax, a is slope).

However, we know that Charles’ law is a special cascade of the ideal gas law.

pV =nRT

T refers to the temperature in kelvin degrees, and V stands for volume.

Furthermore, n represents the number of moles, p represents the pressure of the same material, and R represents the universal ideal gas constant.

The ideal gas law states that

pV = nRT

\begin{aligned}V=\frac{nR}{p}\times T\end{aligned}

\begin{aligned}const= \frac{nR}{p}\end{aligned}

\begin{aligned}const= \frac{nR}{p}\end{aligned} is the slope of the line on the graph in Figure 9.12

therefore, if n doubles, the slope doubles, making the line twice as steep.