In this exercise, we instead consider a form of chemosynthesis. Chemosynthesis is for instance used by microorganisms, whose habitat has very little sunlight such as the deep sea. Here, we focus on chemosynthesis with sulphur, and the corresponding chemical reaction is ₁H₂S + ₂ CO₂ +£3O₂ → £4H₂O +25S+ Cm (H₂O)n. Once again, x, denote the coefficients that balance the equation. If we use the same pro- cedure as in exercise 1 on the reaction in (3), the reduced echelon form of the augmented matrix is 1000-1 0 0100 m 0010-1 -m 0001-1 -n (i) Write out the parametrized solution to the system of equations in (4). (ii) Can we - as in 1(iv) – find a unique solution whenever m and n are known? (iii) Do all solutions (in the mathematical sense) of the system (4) correspond to useable solutions in terms of the chemical equation (3)? 0

Chemistry
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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Exercise 2
In this exercise, we instead consider a form of chemosynthesis. Chemosynthesis is for
instance used by microorganisms, whose habitat has very little sunlight such as the deep
sea. Here, we focus on chemosynthesis with sulphur, and the corresponding chemical
reaction is
₁H₂S + ₂ CO₂ + x3024H₂O +25S + Cm(H₂O)n.
Once again, x, denote the coefficients that balance the equation. If we use the same pro-
cedure as in exercise 1 on the reaction in (3), the reduced echelon form of the augmented
matrix is
[1 0 0 0 -1 0
m
0 1 0 0 0
0 0 10
0001 -1
-m
2
-n
(i) Write out the parametrized solution to the system of equations in (4).
(ii) Can we as in 1(iv) - find a unique solution whenever m and n are known?
(iii) Do all solutions (in the mathematical sense) of the system (4) correspond to useable
solutions in terms of the chemical equation (3)?
Transcribed Image Text:Exercise 2 In this exercise, we instead consider a form of chemosynthesis. Chemosynthesis is for instance used by microorganisms, whose habitat has very little sunlight such as the deep sea. Here, we focus on chemosynthesis with sulphur, and the corresponding chemical reaction is ₁H₂S + ₂ CO₂ + x3024H₂O +25S + Cm(H₂O)n. Once again, x, denote the coefficients that balance the equation. If we use the same pro- cedure as in exercise 1 on the reaction in (3), the reduced echelon form of the augmented matrix is [1 0 0 0 -1 0 m 0 1 0 0 0 0 0 10 0001 -1 -m 2 -n (i) Write out the parametrized solution to the system of equations in (4). (ii) Can we as in 1(iv) - find a unique solution whenever m and n are known? (iii) Do all solutions (in the mathematical sense) of the system (4) correspond to useable solutions in terms of the chemical equation (3)?
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