Question

Suppose now that the container for this sample of helium gas develops a leak overnight while it is fixed at a constant volume. If the gauge pressure of the container drops from 9 to 4 atm during this period while the temperature drops from 27 to insulation to be 3° C., then determine the percentage of the original gas still remaining.

Answer 1

To determine the percentage of the original gas still remaining, we need to calculate the change in the number of moles of gas in the container. We can use the ideal gas law, which states that PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature in Kelvin.

We can rearrange the equation to solve for n: n = PV/RT.

First, let's calculate the original number of moles of gas, n1, using the initial conditions:

P1 = 9 atm

V1 = constant

T1 = 27 + 273 = 300 K

R = 8.31 J/mol K (the ideal gas constant)

n1 = P1V1/RT1 = (9)(constant)/(8.31)(300) = constant/27.29

Next, let's calculate the final number of moles of gas, n2, using the final conditions:

P2 = 4 atm

V2 = constant

T2 = 3 + 273 = 276 K

n2 = P2V2/RT2 = (4)(constant)/(8.31)(276) = constant/23.12

Finally, we can calculate the percentage of the original gas still remaining:

Percentage = (n2/n1) * 100%

= (constant/23.12) / (constant/27.29) * 100%

= 83.72%

So, the answer is that 83.72% of the original gas is still remaining in the container.