Question

There are 10 identical containers of volume V, each of them have an ideal gas at a same temperature T. The first container has a pressure of 1 atm, the second one has a pressure of 2 atm, the third has a pressure of 3 atm and so on. The tenth container has a pressure of 10 atm. If all the 10 containers are connected by thin tubes, then what will be the final pressure (in atm)?

Answer 1

Let the first container contain x mol of gas then PV = xRT i.e. V=xRT as P=1 atm

Then the second container will contain 2x moles, the third will contain 3x moles and so on, the tenth container would contain 10x moles.

When all are connected by the tubes, the total volume would be 10V

The total number of moles of the gas=x+2x+3x+…10x= x$\times \frac{\left(n\right)(n+1)}{2}$, where n = 11
$⟹$ 55x mol

Let the final pressure be $P_t$, then
$P_t\times 10V=55xRT\Rightarrow P_t\times 10V=55V$
$\Rightarrow P_t=5.5\text{atm}$