A cylinder contains 3.5 L of oxygen at 350 K and 2.5 atm . The gas is heated, causing a piston in the cylinder to move outward. The heating causes the temperature to rise to 640 K and the volume of the cylinder to increase to 9.5 L.
What is the gas pressure?
Use the initial set of numbers and the ideal gas law to compute the number of moles, n.
n = PV/(RT)= 2.5*3.5/(0.0826*350)= 0.304 moles
I used R = 0.0826 liter*atm/(mole K)
Then use the ideal gas law again with the above value of n to solve for the unknown P.
P = nRT/V
2.51
2.511
To find the gas pressure in the cylinder after the heating, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = ideal gas constant
T = temperature of the gas
To solve for pressure (P), we need to rearrange the equation to isolate P:
P = (nRT) / V
First, let's calculate the number of moles of gas (n):
We know the initial volume (V1 = 3.5 L), initial temperature (T1 = 350 K), and initial pressure (P1 = 2.5 atm).
Using the ideal gas law, we can calculate n1:
n1 = (P1 * V1) / (R * T1)
Next, we need to calculate the final pressure P2:
V2 = 9.5 L (final volume)
T2 = 640 K (final temperature)
Using the ideal gas law, we can calculate n2:
n2 = (P2 * V2) / (R * T2)
Since the number of moles (n) does not change during this process, we can set n1 equal to n2 and find the pressure (P2) at the final state:
(P1 * V1) / (R * T1) = (P2 * V2) / (R * T2)
Now, let's substitute the known values into the equation and solve for P2:
(2.5 atm * 3.5 L) / (R * 350 K) = (P2 * 9.5 L) / (R * 640 K)
Canceling out the ideal gas constant R, we get:
(2.5 atm * 3.5 L * 640 K) = (P2 * 9.5 L * 350 K)
Now, we can solve for P2:
P2 = (2.5 atm * 3.5 L * 640 K) / (9.5 L * 350 K)
Calculating this expression will give you the value of P2, which is the gas pressure in the cylinder after the heating.