# Determining Gas Constant $R$ from Boyles Law?

I have done an experiment (Boyles Law experiment using Boyles Law Apparatus) in order to determine the value of the gas constant $$R$$. I have also taken into account the dead space volume in my calculations. I am just confused about how I came to my answer there are two ways.

My first method to determine the value of $$R$$ was by doing:

$$R = pVM/mT$$ where I worked out the Molar mass ($$M$$) of air which was 28.97 grams and I used an online converter (Volume to Weight of air) to determine the mass of air which came out to be 0.53 grams. I was told to look for a converter online by one of my lab practitioners to find known weights of air.

This gave my value of $$R$$ to be 7.70 which is not bad considering my uncertainties.

However, my second method of calculating $$R$$ was to do

$$pV = NkT$$ rearranging to $$N = pV/kT$$ which obviously means I'm using the Boltzmann constant. I then subbed my value of N into $$n = N/N_A$$ ($$N_A$$ being Avogadro's constant) and then finally I subbed moles ($$n$$) into $$pV = nRT$$ which then gave my value of $$R$$ to be 8.3106 which is great.

I feel like this result is too good and I might not have a full understanding of the Boltzmann constant or if I'm making unknown assumptions or if it's incorrect. I was hoping some could clarify my results for me as I'm not sure on what to write up.

Any help will be appreciated thank you.

## 1 Answer

I've never used the Boyles Law apparatus so I don't know if $$P$$ was measured too but for comparison of the 2 methods I'm assuming $$P$$ and $$T$$ were both constant.

I immediately see a potential problem with the first method using the value of $$28.97 g/mole$$ for the molar gas volume since this value is for dry air. It's not clear if you dried the air or actually know its composition.

I would expect the second method to be superior to the first method since it uses the measure volume and the well defined constants $$N$$ and $$k$$. It doesn't require knowing the composition of air.