a container with an initial volume of 6 liters at a temperature of 30 degrees celsius with a pressure of 2atm is changed so the temperature is now 90 degrees celsius and the volume is 8 liters. calculate the new pressure
(P1V1/T1) = (P2V2/T2)
Don't forget to convert celsius to kelvin.
To calculate the new pressure of the container, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure (in atm)
V = volume (in liters)
n = moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, let's convert the temperatures from Celsius to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius temperature:
Initial temperature in Kelvin = 30 + 273.15 = 303.15 K
Final temperature in Kelvin = 90 + 273.15 = 363.15 K
Next, we use the ideal gas law equation to compare the initial and final states. Since the moles of gas remain constant and the gas is the same, we can equate the two equations as follows:
P1V1/T1 = P2V2/T2
We can now substitute the known values:
(2 atm) * (6 L) / (303.15 K) = P2 * (8 L) / (363.15 K)
Simplifying the equation further:
12 atm L / 303.15 K = 8 P2 / 363.15 K
Cross-multiply and solve for P2:
(12 atm L * 363.15 K) / (303.15 K) = 8 P2
P2 = (12 * 363.15) / (8 * 303.15)
P2 = 1.5 atm
Therefore, the new pressure, when the volume is 8 liters and the temperature is 90 degrees Celsius, is approximately 1.5 atm.