Hello!
A 22.0 L cylinder containing helium gas at a pressure of 28.1 atm is used to fill a weather balloon in order to lift equipment into the stratosphere. What is the final pressure (in atm) in the cylinder after a 101 L balloon is filled to a pressure of 1.23 atm.
I found the pressure of the gas in the balloon, if it were all in the small cylinder then used Dalton's law of partial pressure to get the final pressure in the small cylinder and got 6.036. This is not right, so can someone help?
Calculate vrms, the root mean square velocity, in m/s of SO2 molecules at 210 oC.
I used the formula, but got a weird answer:5.044x10^11. Help?
Use the van der Waals equation to calculate the pressure, in atm, of 44.75 mol of hydrogen at 64 oC in a 2.15 L container.
This is also an equation problem, but I can't get it. I got the answer to be 575.575.
Thanks in advance!
For the cylinder/balloon problem I would do this.
PV = nRT and calculate mols gas in the cylinder. You have no T listed so use a convenient one and keep it consistent.
Use PV = nRT and solve for mols in the balloon.
Subrtact, initial mols cylinder-mols balloon = mols still in the cylinder.
Then PV = nRT and solve for pressure in the cylinder. I get something like 22 atm (not an exact answer).
Hello! I'd be happy to help you with your questions.
1. To find the final pressure in the cylinder after filling the balloon, you correctly used Dalton's law of partial pressure. The equation to use is P1V1 = P2V2, where P1 and V1 are the initial pressure and volume of the gas in the cylinder, and P2 and V2 are the final pressure and volume of the gas after filling the balloon. Rearranging the equation, we have P2 = (P1V1) / V2.
Given:
Initial pressure (P1): 28.1 atm
Initial volume (V1): 22.0 L
Final volume (V2): 101 L
Balloon pressure (P2): 1.23 atm
Plugging in the values, we get:
P2 = (28.1 atm * 22.0 L) / 101 L
P2 ≈ 6.107 atm
So the final pressure in the cylinder, after filling the balloon, is approximately 6.107 atm.
2. The root mean square velocity (vrms) of gas molecules is calculated using the formula vrms = √((3RT) / M), where R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.
Given:
Temperature (T): 210°C = 210 + 273.15 = 483.15 K
Molar mass of SO2: 64.07 g/mol
Plugging in the values, we get:
vrms = √((3 * 8.314 J/mol·K * 483.15 K) / (64.07 g/mol))
vrms ≈ 507.14 m/s
So the root mean square velocity of SO2 molecules at 210°C is approximately 507.14 m/s.
3. The van der Waals equation accounts for the volume and intermolecular forces of real gases. The equation is: (P + an^2/V^2) × (V - nb) = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, a and b are van der Waals constants, and R is the ideal gas constant.
Given:
Number of moles (n): 44.75 mol
Temperature (T): 64°C = 64 + 273.15 = 337.15 K
Volume (V): 2.15 L
Van der Waals constants for hydrogen: a = 0.2446 atm·L^2/mol^2, b = 0.02661 L/mol
Plugging in the values, we need to solve the equation to find the pressure (P):
(P + (0.2446 atm·L^2/mol^2 * (44.75 mol)^2) / (2.15 L)^2) × (2.15 L - (0.02661 L/mol * 44.75 mol)) = 44.75 mol * 0.0821 atm·L/mol·K * 337.15 K
Simplifying and solving the equation, we get:
P ≈ 2.933 atm
So the pressure of 44.75 mol of hydrogen at 64°C in a 2.15 L container, calculated using the van der Waals equation, is approximately 2.933 atm.
Let me know if you have any further questions!