Question

Calculate the pressure exerted by benzene for a molar volume of 2.10 L at 610. K using the Redlich-Kwong equation of state: P==RTVm−b−aT√1Vm(Vm+b)nRTV−nb−n2aT√1V(V+nb) The Redlich-Kwong parameters a and b for benzene are 452.0 bar⋅dm6⋅mol−2⋅K1/2 and 0.08271 dm3⋅mol−1, respectively. Express your answer with the appropriate units.

Answer 1

`P=21.148 bar`

Step-by-step explanation:

Given parameters are ;

Molar Volume (V_m) = 2.10 L

Temperature (T) = 610 K

a = 452.0 bar dm⁶mol⁻²/
`K^{(1/2)`

b = 0.08271 dm³ mol⁻¹

Our given formula to use is Redlich-Kwong equation of state, which is given as:

`P = (RT)/(V_m-b)-(a)/(√(T) ) *(1)/(V_m(V_m+b)) =(nRT)/(V-nb)-(n^2a)/(√(T) )(1)/(V(V+nb))`

`P = (RT)/(V_m-b)-(a)/(√(T) ) *(1)/(V_m(V_m+b))`

`P = (8.314*10^(-2) bardm^3mol^(-1)k^(-1)*610K)/(2.10dm^3mol^(-1)-0.08271dm^3mol^(-1))-(452bardm^6mol^(-2)K^(1/2))/(√(610K) ) *(1)/(2.10dm^3mol^(-1)(2.10dm^3mol^(-1)+0.08271dm^3mol^-)`

`P = (50.72)/(2.01729)- 18.30095*0.2182`

`P= 25.14-3.992`

`P=21.148 bar`