3) An iron cylinder, with a volume of 20 liters, is filled with 15 moles of prop

Question

3) An iron cylinder, with a volume of 20 liters, is filled with 15 moles of propane.

a. Calculate the pressure inside of the container at -10 degrees Celsius, 10 degrees Celsius, 50 degrees Celsius, 130 degrees Celsius, and 290 degrees Celsius. Plot these values in a graph.

b. Calculate the pressure inside of the container at the indicated temperatures, adjusting for the Van der Waals constant for propane (a = 8.779; b = 0.08445). Plot these values in the previous graph.

c. If the highest pressure that an iron cylinder can tolerate is 35 atm, at what temperature would this cylinder explode?

Explanation / Answer

I will do the values and then, you do the graph.

P1 = 15 * 0.0821 * (263) / 20 = 16.19 atm
P2 = 15 * 0.0821 * (283) / 20 = 17.43 atm
P3 = 15 * 0.0821 * (323) / 20 = 19.89 atm
P4 = 15 * 0.0821 * (403) / 20 = 24.81 atm
P5 = 15 * 0.0821 * (563) / 20 = 34.66 atm

For part c):
T = PV/nR
T = 35 * 20 / 15*0.0821
T = 568.41 K or 295.41 °C

From a higher temperature of 295 °C the cylinder will explode.

Now, The van der walls equation:
(p + a/Vm2)(Vm+b) = RT

Let's calculate Vm: Vm = V/n = 20 / 15 = 1.33 L/mol
(p + 8.779/1.332)(1.33+0.08445) = 0.0821*263
(p + 4.9579)(1.41445) = 21.5923
1.41445p + 7.0127 = 21.5923
1.41445p = 21.5923-7.0127
p = 14.5796/1.41445
p = 10.3076 atm

Now do the same thing with the rest of the temperatures to get the value of p.

Hope this helps

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