After 273 m3 of ethylene oxide at 748 kPa and 525 K is cooled to 293 K, it is allowed to expand to 1100. m3. The new pressure is _____kPa
To find the new pressure, we can use the gas law known as the "ideal gas law," which states that the product of the pressure, volume, and temperature of a gas is constant.
The ideal gas law equation is given as:
PV = nRT
where:
P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature
In this case, we have the initial conditions as follows:
P1 = 748 kPa (initial pressure)
V1 = 273 m3 (initial volume)
T1 = 525 K (initial temperature)
And the final conditions are:
V2 = 1100 m3 (final volume)
T2 = 293 K (final temperature)
We can also assume that the number of moles (n) remains constant.
First, we need to find the number of moles (n) using the ideal gas law equation in the initial conditions:
P1V1 = nRT1
Rearranging the equation, we have:
n = (P1V1) / (RT1)
Next, using the same number of moles (n) in the final conditions, we can find the new pressure (P2):
P2 = (nRT2) / V2
Let's calculate the values step by step:
Step 1: Calculate the number of moles (n) using the initial conditions:
n = (P1V1) / (RT1)
= (748 kPa * 273 m3) / (R * 525 K)
Here, we need the value of the gas constant (R). The value of the gas constant depends on the unit of pressure used. If we assume the pressure is in kilopascals (kPa), then the gas constant R = 8.314 kPa*m3/(mol*K).
Substituting the values, we get:
n = (748 kPa * 273 m3) / (8.314 kPa*m3/(mol*K) * 525 K)
Step 2: Calculate the new pressure (P2) using the final conditions:
P2 = (nRT2) / V2
= ((748 kPa * 273 m3) / (8.314 kPa*m3/(mol*K) * 525 K) * 293 K) / 1100 m3
Now we can simplify this equation and calculate the value of P2.