# Problem evaluating moles in a an isochor transformation

I have a problem with an isochor transformation. Me and my group of study made an experiment that want to check Gay-Lussac’s law. We registered the equilibrium states and fitted the $P = nRT / V$, in the $P(T)$ graph. The moles found are $n_f=(5.63 \times 10^{-3} \pm 1.24 \times 10^{-4})$ mol. The problem is that, initial moles are $n_i=(3.19 \times 10^{-3} \pm 6.97 \times 10^{-5})$ mol. How can the initial moles be smaller?

Details of the experiment: We started stated with a certain number of moles of air inside a metal cylinder closed with a rubber top and connected, through it, to a temperature and pressure sensor. The starting gas conditions are $V, P_0, T_0$ assuming the volume to be constant (the container is, in a good approximation, hermetic).

We heated an amount of water in a calorimeter with a resistance and a temperature $T' \gg T_0$, then we put the cylinder in contact with the hot water plotting the trend of $\Delta P-T$ on a graph. From a certain point the trend gets linear, and with a fit we calculated the slope $m = nR/V$ and from the latter we calculated the number of moles $n$ assuming the air as an ideal gas because of the higher temperature.

We checked the consistency between this value and the one calculated from the initial conditions $n' = P_0V/RT_0$ and surprisingly this value is smaller than the one calculated from the fit. Now what is really happening? the difference $n'-n < 0$ suggests that the number of moles in the cylinder is growing? Or maybe it might be that one of our assumptions is incorrect.

I would independantly check your first result e.g. measure the volume by filling your container with water and measuring the weight change. One mole of an ideal gas is 0.0224m$^3$, so that gives you a third way to calculate the number of moles present.