According to the ideal gas law, a 1.003 mol sample of carbon...

Name: According to the ideal gas law, a 1.003 mol sample of carbon dioxide gas in a 1.561 L container at 270.6 K should exert a pressure of 14.27 atm. What is the percent difference between the pressure calculated using the van der Waals' equation and the ideal pressure? For CO2 gas, a = 3.592 L^2atm/mol^2 and b = 4.267×10^-2 L/mol.
Uploaded: 2023-07-05T14:22:01-08:00
Duration: 6 min
Channel: Cheryl Glor
Description: According to the ideal gas law, a 1.003 mol sample of carbon dioxide gas in a 1.561 L container at 270.6 K should exert a pressure of 14.27 atm. What is the percent difference between the pressure calculated using the van der Waals' equation and the ideal pressure? For CO2 gas, a = 3.592 L^2atm/mol^2 and b = 4.267×10^-2 L/mol.

According to the ideal gas law, a 1.003 mol sample of carbon dioxide gas in a 1.561 L container at 270.6 K should exert a pressure of 14.27 atm. What is the percent difference between the pressure calculated using the van der Waals' equation and the ideal pressure? For CO2 gas, a = 3.592 L^2atm/mol^2 and b = 4.267×10^-2 L/mol.

Transcript

00:01 According to the ideal gas law, 1 .003 moles of carbon dioxide in a container that is 1 .561 liters at a temperature of 270 .6 kelvin should have a pressure that is equal to 14 .27 atmospheres.

00:19 Find the percent difference in the pressure when using the van der waals equation.

00:23 We have a is equal to 3 .592 and b is 4 .267 times 10 to the minus 2.

00:34 Well here we have the van der waals equation as written, but we need to look at pressure.

00:39 So i'm going to go ahead and rearrange this to show the pressure version of it.

00:45 So here we have pressure is equal to the fraction of the number of moles times r times the temperature over volume minus nb minus the fraction an squared over v squared.

00:58 So let's put in some values.

01:01 The number of moles was 1 .003.

01:05 Our r is going to be 0 .08206 and our temperature was given as 270 .6.

01:15 Make that decimal a little bit bigger.

01:17 This is going to be over our volume of 1 .561 liters minus 1 .003, that's the number of moles, times our b value of 4 .267 times 10 to the minus 2.

01:36 Now next is our other fraction where a is 3 .592.

01:45 This is going to be times 1 .003 squared over our volume of 1 .561.

01:55 So quite a bit of math going on.

01:57 So i'm going to break this down into a few different steps.

02:00 Let's first take a look at that first fraction and let's do the numerator.

02:04 We have 1 .003 times 0 .08206 times 270 .6.

02:11 So the first part of our numerator is going to be 22 .272.

02:17 And then i'm going to write out all of the other numbers my calculator gives.

02:23 Now for the denominator, we have 1 .561 minus 1 .003 times 4 .267 times 10 to the minus 2.

02:36 The bottom part is going to be 1 .51820199.

02:43 Now let's take a look at the other fraction.

02:46 1 .003 squared times 3 .592.