Consider 4.50L of a gas at 365 mmHg and 20 degree C . If the container is compressed to 2.70 L and the temperature is increased to 33 degree C , what is the new pressure, P2, inside the container? Assume no change in the amount of gas inside the cylinder.
Use PV = nRT. Don't forget T must be in kelvin, P in atm and V in L.
To solve this problem, we can use the combined gas law, which relates the initial and final conditions of a gas when the amount of gas remains constant. The combined gas law equation is given by:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = Initial pressure
V1 = Initial volume
T1 = Initial temperature
P2 = Final pressure (what we need to find)
V2 = Final volume (given as 2.70 L)
T2 = Final temperature (given as 33 degree C)
Now, let's plug in the given values into the formula and solve for P2:
(P1 * 4.50L) / (20+273)K = (P2 * 2.70L) / (33+273)K
To simplify the equation, we'll convert the temperatures to Kelvin:
20 degree C = 20 + 273 = 293 K
33 degree C = 33 + 273 = 306 K
Now, we can rewrite the equation:
(P1 * 4.50) / 293 = (P2 * 2.70) / 306
Cross-multiplying the equation, we have:
(P1 * 4.50 * 306) = (P2 * 2.70 * 293)
Divide both sides of the equation by (2.70 * 293):
(P1 * 4.50 * 306) / (2.70 * 293) = P2
Simplifying the equation:
P2 = (P1 * 4.50 * 306) / (2.70 * 293)
Now, we can substitute the values into the equation and calculate P2:
P2 = (365 mmHg * 4.50L * 306) / (2.70L * 293)
P2 ≈ 612.45 mmHg
Therefore, the new pressure inside the container (P2) is approximately 612.45 mmHg.
To find the new pressure, P2, inside the container, we can use the combined gas law equation:
P1 * V1 / T1 = P2 * V2 / T2
Where:
P1 is the initial pressure (365 mmHg)
V1 is the initial volume (4.50 L)
T1 is the initial temperature in Kelvin (20°C + 273.15 = 293.15 K)
P2 is the final pressure (we need to find this)
V2 is the final volume (2.70 L)
T2 is the final temperature in Kelvin (33°C + 273.15 = 306.15 K)
We can rearrange the equation to solve for P2:
P2 = (P1 * V1 * T2) / (V2 * T1)
Now we can plug in the values:
P2 = (365 mmHg * 4.50 L * 306.15 K) / (2.70 L * 293.15 K)
Calculating this expression, we find:
P2 = 609.02 mmHg
Therefore, the new pressure, P2, inside the container after compressing it to 2.70 L and increasing the temperature to 33°C is approximately 609.02 mmHg.