A gas bottle contains 0.250 mol of gas at 0.973 bar pressure. If the final pressure is 1.165 bar,
how many moles of gas were added to the bottle?
pressure has increased by a factor of 1.165/0.973 = 1.197
1.197 * 0.250 = 0.299
So, 0.049 mols were added. (Probably 0.05)
Thank you
Thanks
To solve this question, we need to use the ideal gas law equation, which relates the pressure, volume, and number of moles of gas.
The ideal gas law equation is:
PV = nRT,
Where:
P = pressure (in bar),
V = volume (in liters),
n = number of moles,
R = gas constant (0.0821 L•atm/mol•K).
First, let's convert the given pressure values to atmospheres (atm), as the gas constant is given in those units:
0.973 bar × 1 atm/0.9869 bar = 0.987 atm,
1.165 bar × 1 atm/0.9869 bar = 1.18 atm.
Now, we need to rearrange the ideal gas law equation to solve for the number of moles:
n = PV / RT.
Since the final pressure and the volume are constant, and the temperature remains the same (assuming it is constant), we can compare the initial and final number of moles:
n₁ = n₂,
P₁V₁ / RT = P₂V₂ / RT.
Canceling out the common terms, we get:
P₁V₁ = P₂V₂.
Now, let's input the values:
(0.987 atm)(V₁) = (1.18 atm)(V₂).
Since the volume (V₁) is constant, we can assume V₁ = V₂:
(0.987 atm)(V₁) = (1.18 atm)(V₁).
Now, solve for V₁:
V₁ = (1.18 atm)(V₁) / (0.987 atm).
Dividing both sides by V₁, we get:
1 = (1.18 atm) / (0.987 atm).
Simplifying further:
1 = 1.19.
This equation is not possible, as it leads to an inconsistent result. Therefore, there is no solution to this question. It is not possible to determine the number of moles of gas added to the bottle based on the given information.