"A 280ml flask contains pure helium at a pressure of 754 torr . A second flask with a volume of 475ml contains pure argon at a pressure of 732 torr . If the two flasks are connected through a stopcock and the stopcock is opened, what is the partial pressure of helium? What is the partial pressure of argon?"
To find the partial pressure of helium and argon when the two flasks are connected, we can use the ideal gas law.
The ideal gas law is expressed as: PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Since the flasks are connected, the total pressure will be the same in both flasks.
Let's solve for the partial pressures step by step:
Step 1: Convert the pressure from torr to atmospheres.
- 1 atmosphere (atm) = 760 torr (approximately)
Pressure of helium = 754 torr / 760 torr/atm
= 0.9921 atm (rounded to four decimal places)
Pressure of argon = 732 torr / 760 torr/atm
= 0.9632 atm (rounded to four decimal places)
Step 2: Calculate the total number of moles.
- We can use the ideal gas law to find the number of moles in each flask.
For the flask containing helium:
PV = nRT
(0.9921 atm) (0.280 L) = n (0.0821 L.atm/mol.K) (T)
n = (0.9921 atm * 0.280 L) / (0.0821 L.atm/mol.K * T)
For the flask containing argon:
(0.9632 atm) (0.475 L) = n (0.0821 L.atm/mol.K) (T)
n = (0.9632 atm * 0.475 L) / (0.0821 L.atm/mol.K * T)
Note: T is the same for both flasks since they are connected, so T cancels out in the equation.
Since we don't have the temperature (T) given in the question, we cannot determine the number of moles for each flask.
However, we can determine the ratio of the number of moles by assuming the temperature is constant:
n(He) / n(Ar) = (PV)He / (PV)Ar
Let's substitute the known values:
n(He) / n(Ar) = (0.9921 atm * 0.280 L) / (0.9632 atm * 0.475 L)
= 0.2675
The ratio of the number of moles of helium to argon is approximately 0.2675.
Step 3: Calculate the partial pressure of helium and argon.
- Since the total pressure is the same in both flasks, we can set up the equation:
Total pressure = pressure of helium + pressure of argon
Total pressure = P(He) + P(Ar)
From step 1, we know the values of P(He) and P(Ar), we can substitute them into the equation:
Total pressure = 0.9921 atm + 0.9632 atm
= 1.9553 atm (rounded to four decimal places)
Now, we need to find the partial pressures of helium and argon.
The ratio calculated in step 2 indicates that the partial pressure of helium is 0.2675 times the total pressure and the partial pressure of argon is 0.7325 times the total pressure.
Partial pressure of helium = 0.2675 * 1.9553 atm
= 0.5225 atm (rounded to four decimal places)
Partial pressure of argon = 0.7325 * 1.9553 atm
= 1.4328 atm (rounded to four decimal places)
Hence, the partial pressure of helium is approximately 0.5225 atm, and the partial pressure of argon is approximately 1.4328 atm.
To find the partial pressure of helium and argon when the two flasks are connected, we need to apply Dalton's Law of Partial Pressures. According to this law, the total pressure in a mixture of gases is equal to the sum of the partial pressures of each individual gas.
1. First, let's calculate the partial pressure of helium:
- The 280ml flask contains pure helium at a pressure of 754 torr.
- Since the two flasks are connected through a stopcock, the pressure in both flasks will equalize once the stopcock is opened.
- Therefore, the partial pressure of helium in the combined system will still be 754 torr.
2. Now, let's calculate the partial pressure of argon:
- The 475ml flask contains pure argon at a pressure of 732 torr.
- When the stopcock is opened, the pressure in both flasks will equalize.
- So, the partial pressure of argon in the combined system will be 732 torr.
To summarize:
- The partial pressure of helium is 754 torr.
- The partial pressure of argon is 732 torr.
P1V1 = P2V2
He goes from V=280 mL to a total of 755 mL. Calculate P for He.
Same formula for Ar. It goes from 475 mL to 755 mL. Remember Dalton's Law which says that the partial pressure of a gas in a container is independent of any other gases present (as long as they don't react).