Question

Two evacuated bulbs of equal volume are connected by a tube of negligible volume. One of the bulbs is placed in a constant-temperature bath at 245 K and the other bulb is placed in a constant-temperature bath at 350 K . Exactly 5 mol of an ideal gas is injected into the system. Calculate the final number of moles of gas in each bulb.

Answer 1

The final number of moles of gas in each bulb is 2.06 and 2.94 moles.

Step-by-step explanation:

The number of moles can be calculated using Ideal Gas Law:

`PV = nRT` (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:

`n = (PV)/(RT)`

For bulb 1 we have:

`n_(1) = (P_(1)V_(1))/(RT_(1))`

and for bulb 2:

`n_(2) = (P_(2)V_(2))/(RT_(2))`

Dividing n₁ by n₂:

`(n_(1))/(n_(2)) = ((P_(1)V_(1))/(RT_(1)))/((P_(2)V_(2))/(RT_(2)))`

Since V₁ = V₂ and P₁ = P₂ we have:

`(n_(1))/(n_(2)) = ((P_(1)V_(1))/(RT_(1)))/((P_(2)V_(2))/(RT_(2)))`

`(n_(1))/(n_(2)) = (T_(2))/(T_(1)) = (350)/(245) = 1.43`

`n_(1) = 1.43n_(2)` (2)

Also, we have that 5 mol of an ideal gas is injected into the system:

`n_(1) + n_(2) = 5 \rightarrow n_(1) = 5 - n_(2)` (3)

By entering equation (3) into (2) we have:

`5 - n_(2) = 1.43n_(2)`

`n_(2) = 2.06` (4)

(4) into (3):

`n_(1) = 5 - n_(2) = 5 - 2.06 = 2.94`

Therefore, the final number of moles of gas in each bulb is 2.06 and 2.94 moles.

I hope it helps you!