ENGR266 2021 Q3 (ENGR5003)

ENGR266 2021 Q3Past paperOld spec ENGR2662:116 marks19 min

ENGR266 Summer 2021 Q3[PARTIAL] Left out: Part (a) needs Margules activity coefficients (modified Raoult's law), which are not on the current formula sheet (only ideal Raoult's and Henry's laws). Part (b), reaction equilibrium from K, is on-syllabus.

Answer All parts (a) - (b).

Formulas you may need

[EXTERNAL] Modified Raoult's law: $y_i P = x_i \gamma_i P_i^{sat}$ , so $P = x_1\gamma_1 P_1^{sat} + x_2\gamma_2 P_2^{sat}$ (learn this; only ideal Raoult $y_i P = x_i P_i^{sat}$ is on the formula sheet)
[EXTERNAL] Margules equations: $\ln\gamma_1 = x_2^2\left[A_{12} + 2(A_{21} - A_{12})x_1\right]$ , $\ln\gamma_2 = x_1^2\left[A_{21} + 2(A_{12} - A_{21})x_2\right]$ (learn this; not in the current materials)
Equilibrium constant for ideal gases: $K = \prod_i \left(\dfrac{y_i P}{P^\circ}\right)^{\nu_i}$ (on the formula sheet as $K_P = \prod P_i^{\nu_i}$ )
Mole balance with extent of reaction: $n_i = n_{i0} + \nu_i\varepsilon$ , $y_i = n_i/\sum n_i$ (learn this)

(a)
The Methanol(1)/Water(2) system in vapour liquid equilibrium (VLE) can be well described using the combination of Margules equations with parameters $A_{12} = 0.6828$ and $A_{21} = 0.4753$ and the Antoine equations below: $\ln P_1^{sat} = 16.5785 + \dfrac{3{,}638.27}{T/^\circ\mathrm{C} + 239.50}$ $\ln P_2^{sat} = 16.3872 + \dfrac{2{,}885.70}{T/^\circ\mathrm{C} + 230.17}$ Calculate the pressure of the system if Methanol(1)/Water(2) is held in VLE at $60^\circ\mathrm{C}$ and the mole fractions of methyl-ethyl ketone in the liquid and vapour phase are $x_1 = 0.2167$ and $y_1 = 0.6268$ .
P =kPa
[6]
(b(i))
The gas phase reaction between C and H2O can be described as: $C_{(g)} + H_2O_{(g)} \rightarrow CO_{(g)} + H_{2(g)}$ . The reaction takes place at 950 K where the equilibrium constant $K = 1$ and all species can be considered as ideal gases. Assuming a pressure of 1 bar and that the reactants consist of 1 mole of C and 2 moles of H2O, calculate the fraction of steam that reacts.
frac_steam =-
[8]2:2
(b(ii))
How does the fraction of steam that reacts change if the pressure is increased to 20 bar and all other conditions remain the same and why?
frac_steam_20bar =-
[2]Third