Answer:
The final number of moles of gas in each bulb is 2.06 and 2.94 moles.
Explanation:
The number of moles can be calculated using Ideal Gas Law:
[tex] PV = nRT [/tex] (1)
Where:
P: is the pressure
V: is the volume
n: is the number of moles
R: is the ideal gas constant
Solving equation (1) for n:
[tex] n = \frac{PV}{RT} [/tex]
For bulb 1 we have:
[tex] n_{1} = \frac{P_{1}V_{1}}{RT_{1}} [/tex]
and for bulb 2:
[tex] n_{2} = \frac{P_{2}V_{2}}{RT_{2}} [/tex]
Dividing n₁ by n₂:
[tex] \frac{n_{1}}{n_{2}} = \frac{\frac{P_{1}V_{1}}{RT_{1}}}{\frac{P_{2}V_{2}}{RT_{2}}} [/tex]
Since V₁ = V₂ and P₁ = P₂ we have:
[tex] \frac{n_{1}}{n_{2}} = \frac{\frac{P_{1}V_{1}}{RT_{1}}}{\frac{P_{2}V_{2}}{RT_{2}}} [/tex]
[tex] \frac{n_{1}}{n_{2}} = \frac{T_{2}}{T_{1}} = \frac{350}{245} = 1.43 [/tex]
[tex] n_{1} = 1.43n_{2} [/tex] (2)
Also, we have that 5 mol of an ideal gas is injected into the system:
[tex] n_{1} + n_{2} = 5 \rightarrow n_{1} = 5 - n_{2} [/tex] (3)
By entering equation (3) into (2) we have:
[tex] 5 - n_{2} = 1.43n_{2} [/tex]
[tex] n_{2} = 2.06 [/tex] (4)
(4) into (3):
[tex] n_{1} = 5 - n_{2} = 5 - 2.06 = 2.94 [/tex]
Therefore, the final number of moles of gas in each bulb is 2.06 and 2.94 moles.
I hope it helps you!
