Question

A mixture of benzene and toluene are to be separated in a flash tank. The pressure in the flash tank is 800 mm Hg. The units for Antoines equation are mm Hg and ◦C for pressure and temperature, respectively.
xB(Psat B) + (xT)(Psat T) = P
log10(Psat B) = 6.905 − (1211/ (T + 221))
log10(Psat T) = 6.953− (1344/ (T + 219 ))
At what temperature should the tank be operated to get the highest purity toluene in the liquid phase (maximizing xT)?

Answer 1

Answer:

At the temperature of 112.859°C

Explanation:

suppose xT denotes the amount of toluene in the mixture

∴

xT ∈ (0,1)   xB = 1 -xT

substituting the value of xB and re-arrange to solve for xT, we have:

$xT = \dfrac{P-Psat \ B}{P sat \ T - P sat \ B}$

For xT to be maximum, P needs to be equal to Psat T

∴ P = Psat T

or

Psat T = 800

log10 P sat T = log 10(800)

Using MATLAB code to solve the value of T (T_val), the code is inputed as:

syms T

equation = 6.953− (1344/ (T + 219 )) = log 10(800)

T_val = solve (equation,T);

T_val = double T_(val)

T_val= 112.859