Using the equation below calculate the molar volume and...

Using the equation below, calculate the molar volume and compressibility factor for methanol vapor at 500K and 10 bar pressure. As a result of experimental studies, the virial coefficients are as follows: B = -2.19 x 10^-4 m^3/mol, C = -1.73 x 10^-8 m^6/mol^2 Answer the following questions at the critical temperature of methanol at 512.6 K, critical pressure 81 bar. a) Using the virial equation, b) Using the Redlich-Kwong equation.

Transcript

00:01 Welcome here in this question we have two parts.

00:05 So the first thing is using variable equation and the second thing is using radlich norm equation.

00:28 Redlich form equation we had to calculate molar volume and compressibility factor.

00:49 For methanol.

00:53 So this is the question and the given data is a temperature is given 500 kelvin's and pressure is given 10 bar and b value is given minus 2 .19 multiplied by 10 4 meter cube and per mole and c is equal to 1 .73 minus 1 .73 minus 1 .7 7 3 multiplied by 10 power minus 8 meter per 6 and mole square.

01:31 This is the given.

01:36 Answer the following questions at the critical temperature of mitnail at 512 and 81 bar is given.

01:44 So we have here the temperature is given critical temperature.

01:49 So tc is 512 .6 kelvin's and pc is 81 bar.

02:01 Now we will see the question here, a solution for the given question.

02:10 So first thing is by using variable factor equation.

02:23 So it is z is equal to 1 plus b divided by v plus c v squared.

02:33 So let's consider this one as first one.

02:37 And we know that compressibility factor is equal to pv divided by rt.

02:43 So that is equal to 1 plus b divided by v plus c divided by v squared.

02:50 And pv divided by rt is equal to v square plus bv plus c divided by v square we can write.

03:04 When this comes this side p v cube divided by r t is equal to v square plus bv plus c now here v3 p minus v square r t plus r t plus r t is equal to r t bv plus r t is equal to zero so as as all these are in minus condition, we have to take this one in minus only.

03:48 So all are in minus.

03:51 Then here, v -q, p is given 10 bar and minus, sorry, it is minus.

04:02 V is, we have to find out b and r is 8 .314 multiplied by t is given, 4 multiplied by 10 power minus 2 multiplied by 500 is the temperature and minus r is here it is given minus of minus b is the value 2 .19 multiplied by 10 power minus 4 and b we have to find out 8 .314 multiplied by n power minus 2 and 500 is the temperature so b minus of my b b r and here minus c value is given minus 1 .73 multiplied by 10 power minus 8 and r is 8 .3 multiplied by 10 power minus 2 and 500 then all this is equal to 0.

05:16 Then from this one we can get v is equal to 415481 minus 1 .0 multiplied by 10 power minus 5 so then it is equal to v is equal to 4 .158 4 and it is a molar volume.

05:47 Now, z is equal to 1 plus b divided by b plus c divided by v squared.

05:57 So by substituting these values, b is minus 2 .19 multiplied by 10 power minus 4 divided by volume is 4 .1548 multiplied minus 1 .73 multiplied by 10 power minus 8 divided by 4 .73 multiplied by 10 power minus 8 divided by 4.

06:17 4 .154181 whole square...

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