The Rankine temperature scale used in engineering is to the
Fahrenheit scale as the Kelvin scale is to the Celsius scale.
That is, 1 Rankine degree is the same size as 1 Fahrenheit
degree, and 0 °R = absolute zero.
(b) What is the value of the gas constant R on the Rankine
scale in 1L ~ atm21°R ~ mol2?
(c) Use the van der Waals equation to determine the pressure
inside a 400.0-mL vessel that contains 2.50 mol of
CH4 at a temperature of 525 °R. For CH4, a = 2.253
1L2 ~ atm2mol2 and b = 0.04278 Lmol.

Question

The Rankine temperature scale used in engineering is to the 
Fahrenheit scale as the Kelvin scale is to the Celsius scale. 
That is, 1 Rankine degree is the same size as 1 Fahrenheit 
degree, and 0 °R = absolute zero. 
(b) What is the value of the gas constant R on the Rankine 
scale in 1L ~ atm2>1°R ~ mol2? 
(c) Use the van der Waals equation to determine the pressure 
inside a 400.0-mL vessel that contains 2.50 mol of 
CH4 at a temperature of 525 °R. For CH4, a = 2.253 
1L2 ~ atm2>mol2 and b = 0.04278 L>mol.

Accepted Answer

Hi everyone. This problem reads the Rankine scale used in engineering is similar to the kelvin scale. Where degrees are is also absolute zero, calculate the pressure of 1.10 moles of helium in a 300 millimeter container at 650 degrees Are the value of our using atmospheres and degree are is 6500. 30 to 4 atmospheres per cubic feet over pound mold degrees are for helium A is equal to 40.341 atmospheres times leader squared over mold squared and B is equal to 0. liters over mold. So our goal here is to calculate pressure. Okay. And based off of what's given in the problem, we're going to need to use the Vander wal's equation to calculate the pressure and the Vander wal's equation for calculating pressure is P is equal to N R T over v minus n b minus a N squared over V squared. Okay, so this is our Van der Waals equation and let's take a look at what we need. All right, so N represents moles and were given the amount of moles in the problem. We're told we have 1.10 moles of helium. Alright, R is the gas constant and this is a value that we should know. It's 0.8 to 06. So let's go ahead and write down all of our values. Okay, so we know n is equal to 1. moles. R is equal to 0.8 to 06 Leaders atmosphere over old times kelvin that is a constant. Okay, T is equal to temperature. Okay, in the problem, we're told that The temperature is 650 degrees are alright, so we'll go ahead and write that here. Alright. V represents volume. And in the problem we're told the volume is, let's take a look. It's 300 mL. So we're going to want to convert this milliliters to leaders. So we're going to divide by 1000. So our volume is going to be 0.300 L. Okay. And were given the constants A and B. And the values for them. Okay, so we have a Vander Wal's constant a is 0. atmospheres Leader squared over moles squared and Vander wal's constant B is equal to 0.238 Leaders over mole. Okay, so four R R. We're giving it an for our our we need to convert this the value for our using A T. M. And actually this are the value that we're going to use is the one that was given in the problem. Excuse me. So the value for this are is 0. 30- atmospheres cubic feet over pound. No degrees are Okay. So the units for this is not the units that we're going to want to use to plug into our Van der Waals equation. We're going to need to convert this value of R two units of atmosphere Leader over moles, times degree are alright, so let's go ahead and do that conversion down here below. Okay, so we're going to take our our value The way that it's given. So we have 0.730- atmosphere cubic feet over pound mo degree are Okay, so our goal here is to go from the units of atmosphere cubic feet over pound mole degree are we want to go from that to atmosphere leaders over mole degree are so that is the correct units that we want. So let's go ahead and convert the first thing we're going to do is we're going to convert the cubic feet to leaders. Okay, So in one cubic feet There is 28 leaders, so cubic feet cancel. Okay, now we want to go from pound moles to moles. Okay, And the conversion for that is £1 mole Is equal to 453. moles. Okay, so our units of pound mold cancel and now we're in the units that we want. So let's do the math or let's do the calculation and when we do the calculation, we get 0. atmosphere leaders over more degree are okay, so that is our value for R So now we have everything that we need so we can plug it in to our Vander wal's equation. So let's go ahead and do that now. Okay, so let's go ahead and clear some space so that we can have enough room to plug in everything. Okay, so we have pressure Is equal to n r. number of moles is 1.10 moles are is that new value for our we just calculated which is 0. atmosphere leaders over more degree are And temperature is 650° are okay and this is all over. V volume is 0. liters. So b minus N. Which is our number of moles is 1.10 moles times B R. Vander wal's constant B is 0. leaders over more. So that's v minus n B minus A or Vander wal's constant A is equal to zero point atmospheres leaders squared over moles squared. So that's our Vander wal's constant a times our moles squared, so 1.1 zero moles squared and this is over V squared. So our volume is 0.300 liters. Okay, So now what we're going to do is do the calculation so we can solve for the pressure. Okay, so once we do this calculation we will get a pressure of 118. atmospheres and this is going to be our final answer. Okay, so this is going to be the pressure that is calculated and we did that by using the Vander wal's equation. Okay, so that is it for this problem. I hope this was helpful.

Verified Solution

Key Concepts

Gas Constant (R)

Van der Waals Equation

Temperature Scales