The final pressure is 420 Torr.
When we connect the bulbs, the total volume V_"tot" of the system is
V_"tot" = (1.0 + 1.0 + 0.5) L = 2.5 L
No we can use Boyle's Law to calculate the partial pressure of each gas after it has expanded into the new volume.
For N₂: P_2 = P_1 × V_1/V_2 = 635"Torr" × (1.0"L")/(2.5"L") = 254 Torr (2 significant figures)
For Ne: P_2 = P_1 × V_1/V_2 = 212"Torr" × (1.0"L")/(2.5"L") = 84.8 Torr (2 significant figures)
For H₂: P_2 = P_1 × V_1/V_2 = 418"Torr" × (0.5"L")/(2.5"L") = 83.6 Torr (1 significant figure)
Each gas exerts it pressure independently of the others, so we can apply Dalton's Law of Partial Pressures.
P_"tot" = P_"N₂" + P_"Ne" + P_"H₂" = (254 + 84.8 + 83.6) Torr = "422.4"Torr = 420 Torr (2 significant figures)
