Chapter 5, Problem 33QAP

7) You are tasked with separating two proteins by ion exchange chromatography on a 30 cm long column with an inner diameter of 2 cm. The resin has a diameter of 100 μm and a void fraction of 0.3, and your mobile phase flows through the column at a rate of Q = 5 cm³/min. The Van Deemter coefficients A, B, and C have been determined to be 0.0228 cm, 0.0036 cm²/min, and 0.00053 min, respectively, for both proteins. Protein A elutes from the column with an average retention time of 27 min and standard deviation of 0.8 min. Protein B elutes from the column. with an average retention time of 33.8 min and standard deviation of 1.0. a) How many theoretical plates does the column contain? b) What flow rate (Q) will give you the maximum resolution? c) What is the minimum height of a theoretical plate for the system?

.NET Interactive Solving Sudoku using Grover's Algorithm We will now solve a simple problem using Grover's algorithm, for which we do not necessarily know the solution beforehand. Our problem is a 2x2 binary sudoku, which in our case has two simple rules: •No column may contain the same value twice •No row may contain the same value twice If we assign each square in our sudoku to a variable like so: 1 V V₁ V3 V2 we want our circuit to output a solution to this sudoku. Note that, while this approach of using Grover's algorithm to solve this problem is not practical (you can probably find the solution in your head!), the purpose of this example is to demonstrate the conversion of classical decision problems into oracles for Grover's algorithm. Turning the Problem into a Circuit We want to create an oracle that will help us solve this problem, and we will start by creating a circuit that identifies a correct solution, we simply need to create a classical function on a quantum circuit that…

4) A fixed bed adsorption unit contains rigid (incompressible) silica particles with a diameter of 120 um and porosity of 0.3. The resin bed is 200 cm long and has a diameter of 15 cm. A protein solution is pumped into the column at a rate of 50 L/min, and the mobile phase has a viscosity of 1.2 CP. a) What is the pressure drop for this system (in bar)? b) What would be the pressure drop if the particle diameter were decreased to 30 μm?