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First, we need to find the total volume of the container when the gases are allowed to mix. Since the volume of the tube is negligible, the total volume will be the sum of the initial volumes of Ne and He:
Total volume = 5.00 L + 3.00 L = 8.00 L
Next, we can use the combined gas law to find the final pressure of Ne:
(P1)(V1) = (P2)(V2)
P1 = 654 mmHg
V1 = 5.00 L
V2 = 8.00 L (total volume)
P2 = final pressure of Ne
Plugging in the values:
(654 mmHg)(5.00 L) = (P2)(8.00 L)
3270 mmHg*L = 8P2
P2 = (3270 mmHg*L) / 8 L
P2 = 408.75 mmHg
Therefore, the final pressure of Ne is 408.75 mmHg.