Solve the following system of equations $$4x_1 + 5x_2 = 6$$ $$3x_1-2x_2 = 14 $$

Let us use $$ A x = b$$ expression to solve the problem. Thus $$ A = [4, 5; 3, -2]$$ $$ b = [6; 14] $$ Thus the solution will be $$x = A\b$$

A liquid-phase mixture consists of 65% of component A and 35% of B, with a feed molar flowrate of $$F_0$$ kmol/h. It is flashed a temperature T. Calculate the limits of pressure where exists two phases in equilibrium. Assuming the saturation pressure for A and B at temperature T are known.

In this kind of problem, you should calculate the dew (minimum) and bubble (maximum) pressure. The bubble pressure is calculate from: $(P_b = z_1 P_1^{sat} + z_2 P_2^{sat} $) while dew pressure is $(P_d = \cfrac{1}{\cfrac{z_1}{ P_1^{sat}} + \cfrac{z_2}{ P_2^{sat}} }$)

What is the volume of an ideal plug-flow reactor required to achieve a fractional conversion of 85% of A. Assuming that the feed molar flow of A is 10 kmol/s, the feed concentration of A is 1 mol/L, the reaction is first-order and the reactor operates isothermally, and the kinetic rate constant $$k$$ is equal to 10 1/s. The reaction is $( A \rightarrow B $)

In this case, you should solve the equation design for this kind of reactor. The equation to be solve is: $( \frac{dX_A}{dV} = k \frac{C_{Ao}(1 - X_A)}{F_{Ao}} $) The initial condition is $X_A = 0$ when $V = 0$