# Question #3efe3

Dec 17, 2014

Boyle's law states that the pressure and the volume of a gas are proportional to one another, if temperature and the number of moles are kept constant.

Starting from the ideal gas law, $P V = n R T$, and taking into account the premise that moles and temperature are kept constant, we get

$V = \frac{1}{P} \cdot n R T \to V = \frac{1}{P} \cdot k$, where

$k = n R T = c o n s t a n t$

Now, a plot of $V$ vs $\frac{1}{P}$ will look like this (the graph on the right)

Notice that the line starts from the origin, which is consistent with the premise that $b = 0 \to$ from $y = m x + b$

SInce your linear equation is given,

$y = 2060.1 x + 2 \cdot {10}^{- 5}$, we can assume that $2 \cdot {10}^{- 5}$ is negligible; all you need now is a second point on the line in order to express the slope. The most obvious point on this graph is $\left(0 , 0\right)$, which will give

$m = \frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}} = \frac{3.1146 - 0}{0.001526618 - 0} = 2040.2$, which represents the slope of the graph $V$ vs $\frac{1}{P}$, and the constant $k = n R T$.