A gas is heated from 298 K to 367 K while its volume changes from 2.5 L to 3.9 L. If the initial pressure of the gas is 1.1 atm, what is the final pressure of the gas?
P V = n R T
n and R are constant here.
So
P2 V2 / T2 = P1 V1 / T1
P2 * 3.9 / 367 = 1.1 * 2.5 / 298
P2 = 1.1 * 367/298 * 2.5/3.9
0.868 atm
To find the final pressure of the gas, we can use the combined gas law equation:
P1V1 / T1 = P2V2 / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (what we want to find)
V2 = final volume
T2 = final temperature
Given:
P1 = 1.1 atm
V1 = 2.5 L
T1 = 298 K
V2 = 3.9 L
T2 = 367 K
Plugging in the values, we get:
(1.1 atm * 2.5 L) / 298 K = (P2 * 3.9 L) / 367 K
Now, we can solve for P2, which is the final pressure:
(2.75 atm·L) / 298 K = (3.9 P2) / 367 K
Cross multiplying, we have:
(2.75 atm·L * 367 K) = (3.9 P2 * 298 K)
Dividing both sides by (3.9 * 298 K), we get:
(2.75 atm·L * 367 K) / (3.9 * 298 K) = P2
After evaluating the expression, we find:
P2 ≈ 3.26 atm
Therefore, the final pressure of the gas is approximately 3.26 atm.
To find the final pressure of the gas, we can use the combined gas law equation, which relates the initial and final conditions of temperature, volume, and pressure for a gas sample. The combined gas law equation is given by:
(P1 * V1) / T1 = (P2 * V2) / T2
where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures in Kelvin.
Let's plug in the given values:
P1 = 1.1 atm (initial pressure)
V1 = 2.5 L (initial volume)
T1 = 298 K (initial temperature)
V2 = 3.9 L (final volume)
T2 = 367 K (final temperature)
Now we can solve for P2, the final pressure.
(P1 * V1) / T1 = (P2 * V2) / T2
(1.1 atm * 2.5 L) / 298 K = (P2 * 3.9 L) / 367 K
(2.75 atm L) / 298 K = (P2 * 3.9 L) / 367 K
Cross-multiplying, we have:
2.75 atm L * 367 K = P2 * 3.9 L * 298 K
Using a calculator, we can find:
P2 * 1140.25 atm L = 11448.2 atm L
Dividing both sides by 1140.25 atm L, we get:
P2 = 10.04 atm
Therefore, the final pressure of the gas is approximately 10.04 atm.