I'm having trouble understanding Boyle's Law and Dalton's law of partial pressures. Can anyone help me work this please? Thank you
A sample of propane gas, C3H8, was collected over water at 22.5 ºC and 680. torr. The volume of the wet gas is 3.89 L. What will be the volume of the dry propane at standard pressure?
Ptotal = pC3H8 + pH2O
You know Ptotal is 680. Look up the vapor pressure of H2O in tables (from your text or otherwise), substitute and solve for pC3H8. That will be dry C3H8 at the conditions listed. Then use (P1V1/T1) = (P2V2/T2) to convert to standard conditions.
To solve this problem, we need to apply Boyle's Law and Dalton's Law of Partial Pressures.
Boyle's Law states that the volume of a gas is inversely proportional to its pressure, assuming temperature and amount of gas remain constant. Mathematically, Boyle's Law can be expressed as:
P1 * V1 = P2 * V2
Where P1 and V1 are the initial pressure and volume, respectively, and P2 and V2 are the final pressure and volume.
In this case, we are given the initial pressure (680 torr) and volume (3.89 L). We want to find the final volume, which will be at standard pressure (1 atm). Since we are only provided with the initial pressure and volume, we can rearrange Boyle's Law equation to solve for V2:
P1 * V1 = P2 * V2
V2 = (P1 * V1) / P2
Now, we need to consider Dalton's Law of Partial Pressures. According to this law, the total pressure of a gas mixture is the sum of the partial pressures of each gas in the mixture. The partial pressure of a gas is the pressure it would exert if it occupied the same volume alone at the same temperature. Mathematically, Dalton's Law can be expressed as:
P_total = P_gas1 + P_gas2 + P_gas3 + ...
In this case, we have a mixture of propane gas and water vapor. The pressure measured (680 torr) includes the partial pressure of water vapor. We want to find the volume of dry propane at standard pressure, so we need to subtract the partial pressure of water vapor from the total pressure.
To determine the partial pressure of water vapor, we can use the vapor pressure of water at 22.5 ºC, which can be found in a reference table. At this temperature, the vapor pressure of water is approximately 19.8 torr.
Using Dalton's Law, we can write:
P_propane + P_water = P_total
Since we want to find the volume of the dry propane at standard pressure, we can rewrite this equation as:
P_propane = P_total - P_water
Now that we have the partial pressure of propane gas, we can substitute it into Boyle's Law equation to find the volume of the dry propane gas at standard pressure.
V2 = (P1 * V1) / P2
Let's substitute the values provided into these equations to find the final answer.