Container A holds 752 mL of ideal gas at 2.40 atm. Container B holds 179 mL of ideal gas at 4.80 atm. If the gases are allowed to mix together, what is the resulting pressure?
Note: Find the partial pressure of each gas in the total volume using a formula that relates volume and pressure. Then sum the partial pressures to get the total pressure.
I am having trouble trying to figure out what formula I can use to determine the partial pressure of each. Is it Boyle's Law?
P1V1 = P2V2 for gas 1.
P1V1 = P2V2 for gas 2.
Total P = 1 + 2 = ? (not 3 :-).
So would it look like this:
2.40*752=P2*931 for gas 1
4.80*179=P2*931 for gas 2
Then add the two P2's that I get. Right?
You have it.
Makes sense now. Thank you.
To find the resulting pressure when the gases in container A and B mix together, we need to calculate the partial pressure of each gas and then sum them up to obtain the total pressure.
First, let's calculate the partial pressure for each gas using the formula (P1 * V1 = P2 * V2), where P1 and V1 are the initial pressure and volume of the gas, and P2 and V2 are the final pressure and volume after mixing.
For container A, we have:
P1A = 2.40 atm (initial pressure)
V1A = 752 mL (volume)
Now, referring to the mixed volume:
P2A = ? (partial pressure of gas A in the mixed volume)
V2A = V1A + V1B (total mixed volume)
Similarly, for container B:
P1B = 4.80 atm (initial pressure)
V1B = 179 mL (volume)
Again, referring to the mixed volume:
P2B = ? (partial pressure of gas B in the mixed volume)
V2B = V1A + V1B (total mixed volume)
Since the gases are allowed to mix together, the total mixed volume is given by the sum of the individual volumes from container A and B.
V2A = V2B = V1A + V1B = 752 mL + 179 mL = 931 mL
Now, we can substitute the known values in the formula to calculate the partial pressures:
P1A * V1A = P2A * V2A
2.40 atm * 752 mL = P2A * 931 mL
1804.8 = P2A * 931
P2A = 1804.8 / 931
P2A ≈ 1.94 atm (partial pressure of gas A)
Similarly, we can calculate the partial pressure of gas B:
P1B * V1B = P2B * V2B
4.80 atm * 179 mL = P2B * 931 mL
859.2 = P2B * 931
P2B = 859.2 / 931
P2B ≈ 0.92 atm (partial pressure of gas B)
Now, to find the resulting pressure when the gases mix together, we can sum up the partial pressures:
Total Pressure = P2A + P2B = 1.94 atm + 0.92 atm
Total Pressure ≈ 2.86 atm
Therefore, the resulting pressure when the gases in container A and B mix together is approximately 2.86 atm.