Three bulbs are filled with CH$$_4$$, CO$$_2$$ and Ne as shown in the picture. The bulbs are connected through pipes of zero volume. When the stopcocks are opened and the temperature is kept constant throughout, the pressure of the system is found to be ______ atm. (Nearest integer).

Since the connecting glass pipes add zero dead volume, the final total volume is the absolute sum of all individual gas chambers:

The consolidated equation used to find the final pressure of non-reacting mixed gases is:

Substitute our exact values directly into the core formula:

$$P_{\text{total}} \times 9 = (2 \times 2) + (4 \times 3) + (3 \times 4)$$
$$P_{\text{total}} \times 9 = 4 + 12 + 12$$
$$P_{\text{total}} \times 9 = 28$$
$$P_{\text{total}} = \frac{28}{9} \approx 3.11\text{ atm}$$

The precise value yields 3.11 atm. Rounding off to the closest whole integer gives us 3.