Consider 4.80 L of a gas at 365 mmHG and 20 c. . If the container is compressed to 2.90 L and the temperature is increased to 36 c , what is the new pressure, , inside the container? Assume no change in the amount of gas inside the cylinder
(P1V1/T1) = (P2V2/T2)
Remember T1 and T2 must be in kelvin.
To solve this problem, we can use the combined gas law equation, which relates the initial and final conditions of pressure, volume, and temperature:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (unknown)
V2 = final volume
T2 = final temperature
Let's substitute the given values into the equation:
P1 = 365 mmHg
V1 = 4.80 L
T1 = 20 °C + 273.15 = 293.15 K
V2 = 2.90 L
T2 = 36 °C + 273.15 = 309.15 K
Now, we can solve for P2:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
P2 = (P1 * V1 * T2) / (V2 * T1)
P2 = (365 mmHg * 4.80 L * 309.15 K) / (2.90 L * 293.15 K)
Simplifying the equation:
P2 = (378285.12 mmHg * K) / (846.335 mmHg * K)
P2 = 447.41 mmHg
Therefore, the new pressure inside the container is approximately 447.41 mmHg.
To find the new pressure inside the container, you can use the combined gas law equation, which combines Boyle's law, Charles's law, and Gay-Lussac's law. The formula is as follows:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (what we're trying to find)
V2 = final volume
T2 = final temperature
Let's plug in the given values:
P1 = 365 mmHg
V1 = 4.80 L
T1 = 20 °C + 273.15 = 293.15 K
V2 = 2.90 L
T2 = 36 °C + 273.15 = 309.15 K
Substituting these values into the combined gas law formula:
(365 mmHg * 4.80 L) / (293.15 K) = (P2 * 2.90 L) / (309.15 K)
Now, we can solve for P2:
(365 mmHg * 4.80 L * 309.15 K) / (293.15 K * 2.90 L) = P2
Calculating this equation will give you the value of P2, which is the new pressure inside the container when it is compressed to 2.90 L and the temperature is increased to 36 °C.