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.