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As a chemical engineer in an analytical equipment company, you have designed hollow polymeric microspheres to be used as reactors to replicate DNA sequences in a Polymerase Chain Reaction (PCR) system. The interior of the microspheres have been filled with all the necessary PCR reactants in solution, which have been named as reactant B. In using this PCR system, the user will just have to prepare a beaker of the sample DNA at 10 μM and place the microspheres into the beaker. The sample DNA concentration will be at a constant 50 µm from the surface of the microsphere, and form a concentration gradient to the surface for diffusion into the microsphere where it will react. It is assumed that this concentration gradient will reach steady-state very quickly, and that no mixing of the solution in the beaker is necessary. It is given that the diffusivity of DNA in the solution and inside the microsphere is 10-11 m²/s, and the microsphere has a diameter of 350 μm. The rate of the PCR reaction, DNA + B → product, is given by the equation ro = -kд, where kд = 71 pM/s. (a) Draw the two mass transfer systems involved in this PCR process as described above, and state the assumptions for each. (b) What is the concentration of DNA at the surface of the microsphere if the total rate of mass transfer of DNA from the solution into the microsphere is 2.2x10-20 mol·m².s¨¹? (c) What is the concentration of DNA at the centre of the microsphere? Is this system reaction controlled or diffusion controlled? To have a successful PCR reaction to produce sufficient amount of replicated DNA, the minimum concentration of DNA needed is 10 μM. How long will the PCR reaction take?

As a chemical engineer in an analytical equipment company, you have designed hollow polymeric microspheres to be used as reactors to replicate DNA sequences in a Polymerase Chain Reaction (PCR) system. The interior of the microspheres have been filled with all the necessary PCR reactants in solution, which have been named as reactant B. In using this PCR system, the user will just have to prepare a beaker of the sample DNA at 10 μM and place the microspheres into the beaker. The sample DNA concentration will be at a constant 50 µm from the surface of the microsphere, and form a concentration gradient to the surface for diffusion into the microsphere where it will react. It is assumed that this concentration gradient will reach steady-state very quickly, and that no mixing of the solution in the beaker is necessary. It is given that the diffusivity of DNA in the solution and inside the microsphere is 10-11 m²/s, and the microsphere has a diameter of 350 μm. The rate of the PCR reaction, DNA + B → product, is given by the equation ro = -kд, where kд = 71 pM/s. (a) Draw the two mass transfer systems involved in this PCR process as described above, and state the assumptions for each. (b) What is the concentration of DNA at the surface of the microsphere if the total rate of mass transfer of DNA from the solution into the microsphere is 2.2x10-20 mol·m².s¨¹? (c) What is the concentration of DNA at the centre of the microsphere? Is this system reaction controlled or diffusion controlled? To have a successful PCR reaction to produce sufficient amount of replicated DNA, the minimum concentration of DNA needed is 10 μM. How long will the PCR reaction take?

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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As a chemical engineer in an analytical equipment company, you have designed hollow polymeric microspheres to be used as reactors to replicate DNA sequences in a Polymerase Chain Reaction (PCR) system. The interior of the microspheres have been filled with all the necessary PCR reactants in solution, which have been named as reactant B. In using this PCR system, the user will just have to prepare a beaker of the sample DNA at 10 μM and place the microspheres into the beaker. The sample DNA concentration will be at a constant 50 µm from the surface of the microsphere, and form a concentration gradient to the surface for diffusion into the microsphere where it will react. It is assumed that this concentration gradient will reach steady-state very quickly, and that no mixing of the solution in the beaker is necessary. It is given that the diffusivity of DNA in the solution and inside the microsphere is 10-11 m²/s, and the microsphere has a diameter of 350 μm. The rate of the PCR reaction, DNA + B → product, is given by the equation ro = -kд, where kд = 71 pM/s. (a) Draw the two mass transfer systems involved in this PCR process as described above, and state the assumptions for each. (b) What is the concentration of DNA at the surface of the microsphere if the total rate of mass transfer of DNA from the solution into the microsphere is 2.2x10-20 mol·m².s¨¹? (c) What is the concentration of DNA at the centre of the microsphere? Is this system reaction controlled or diffusion controlled? To have a successful PCR reaction to produce sufficient amount of replicated DNA, the minimum concentration of DNA needed is 10 μM. How long will the PCR reaction take?
Transcribed Image Text:As a chemical engineer in an analytical equipment company, you have designed hollow polymeric microspheres to be used as reactors to replicate DNA sequences in a Polymerase Chain Reaction (PCR) system. The interior of the microspheres have been filled with all the necessary PCR reactants in solution, which have been named as reactant B. In using this PCR system, the user will just have to prepare a beaker of the sample DNA at 10 μM and place the microspheres into the beaker. The sample DNA concentration will be at a constant 50 µm from the surface of the microsphere, and form a concentration gradient to the surface for diffusion into the microsphere where it will react. It is assumed that this concentration gradient will reach steady-state very quickly, and that no mixing of the solution in the beaker is necessary. It is given that the diffusivity of DNA in the solution and inside the microsphere is 10-11 m²/s, and the microsphere has a diameter of 350 μm. The rate of the PCR reaction, DNA + B → product, is given by the equation ro = -kд, where kд = 71 pM/s. (a) Draw the two mass transfer systems involved in this PCR process as described above, and state the assumptions for each. (b) What is the concentration of DNA at the surface of the microsphere if the total rate of mass transfer of DNA from the solution into the microsphere is 2.2x10-20 mol·m².s¨¹? (c) What is the concentration of DNA at the centre of the microsphere? Is this system reaction controlled or diffusion controlled? To have a successful PCR reaction to produce sufficient amount of replicated DNA, the minimum concentration of DNA needed is 10 μM. How long will the PCR reaction take?
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