Question # $1(40$ Points$)$

Chemical engineers often are required to calculate the bubble point of a liquid mixture. For instance, let us examine the bubble point of a mixture of $40\mathrm{.}0\%$ benzene $($B$)$ and $60\mathrm{.}0\%$ toluene $(T)$ at atmospheric pressure $(760mmHg).$ As the mixture temperature gets higher, the vapor pressure exerted by both liquids rises, also, until the bubble point $($the first bubble of vapor$)$ is reached. The vapor pressure of benzene plus the vapor pressure of toluene will equal atmospheric pressure $(760mmHg).$ The equation for the bubble point for this mixture is:

$f(T_{bp})=0\mathrm{.}400**p_b(T_{bp})+0\mathrm{.}600**p_t(T_{bp})-760=0$

where $T_{bp}$ is the bubble point temperature

$p_b$ is the pressure exerted by the benzene, calculated by the Antoine equation below

$p_t$ is the pressure exerted by the toluene, calculated by the Antoine equation below

The Antoine equation expresses the vapor pressure of a substance as:

$lo{g}_{10}p=A-(\frac{B}{T+C}),$ where $A,B,$ and $C$ are constants unique to each chemical species

T is the temperature in Kelvin, so add $273\mathrm{.}15$ to your first guess of the bubble point temperature. The units of pressure are $mmHg.$ The constants for each chemical are:

Benzene: $A=6\mathrm{.}89272,B=1203\mathrm{.}531,C=219\mathrm{.}888$

Toluene: $A=6\mathrm{.}95805,B=1346\mathrm{.}773,C=219\mathrm{.}693$

Calculate the bubble point temperature of this mixture $($K$)$ using either Goal Seek or Solver $($you choose$).$ Include the units of temperature.

using Excel