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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.

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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.

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