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4. This exercise will show an application of spanning sets and linear independence to Chemistry. In industrial production or in theoretical Chemistry, you may encounter processes that need multiple reactions in order to be achieved. Nevertheless, sometimes, the list of reactions is longer than needed since it has redundant steps. Although this sounds weird, it is not easy to differentiate which reactions are not needed. We will work with the following reactions: 1 CO +O2 → CO2 H2 +O2 → H2O 2 3 CH4 +O2 → CO + 2H2O CH4 + 202 → CO2+2H2O (a) Write all of these reactions as equations. For example 1 CO + O2 → CO2 can be written as CÓ+ = CO2. (b) Order the system of equations in such a way that each equation equal 0. For example, CO+ = CO2 should be written as Co +02 – CO2 = 0. CO + - co (c) Consider each chemical compound as a variable. Taking that into account, write the matrix associated to this system of equations. HINT: You should have 6 variables.

4. This exercise will show an application of spanning sets and linear independence to Chemistry. In industrial production or in theoretical Chemistry, you may encounter processes that need multiple reactions in order to be achieved. Nevertheless, sometimes, the list of reactions is longer than needed since it has redundant steps. Although this sounds weird, it is not easy to differentiate which reactions are not needed. We will work with the following reactions: 1 CO +O2 → CO2 H2 +O2 → H2O 2 3 CH4 +O2 → CO + 2H2O CH4 + 202 → CO2+2H2O (a) Write all of these reactions as equations. For example 1 CO + O2 → CO2 can be written as CÓ+ = CO2. (b) Order the system of equations in such a way that each equation equal 0. For example, CO+ = CO2 should be written as Co +02 – CO2 = 0. CO + - co (c) Consider each chemical compound as a variable. Taking that into account, write the matrix associated to this system of equations. HINT: You should have 6 variables.

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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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4. This exercise will show an application of spanning sets and linear independence to Chemistry. In industrial production or in theoretical Chemistry, you may encounter processes that need multiple reactions in order to be achieved. Nevertheless, sometimes, the list of reactions is longer than needed since it has redundant steps. Although this sounds weird, it is not easy to differentiate which reactions are not needed. We will work with the following reactions: CO +02 → CO2 H2 + 02 → H2O 3 CH4 +O2 → CÓ + 2H2O 2 CHA + 202 → CO2+2H2O (a) Write all of these reactions as equations. For example 1 CO +02 → CO2 can be written as 1 co +02 = CO,. (b) Order the system of equations in such a way that each equation equal 0. For example, 1 CO +02 = CO2 should be written as CO +02 - CO2 = 0. (c) Consider each chemical compound as a variable. Taking that into account, write the matrix associated to this system of equations. HINT: You should have 6 variables. (d) For this matrix, find an spanning set for the row space. (e) Remember that each of this vectors represents an equation. Write the equations that are "independent" between them. HINT: You get three at the end.
Transcribed Image Text:4. This exercise will show an application of spanning sets and linear independence to Chemistry. In industrial production or in theoretical Chemistry, you may encounter processes that need multiple reactions in order to be achieved. Nevertheless, sometimes, the list of reactions is longer than needed since it has redundant steps. Although this sounds weird, it is not easy to differentiate which reactions are not needed. We will work with the following reactions: CO +02 → CO2 H2 + 02 → H2O 3 CH4 +O2 → CÓ + 2H2O 2 CHA + 202 → CO2+2H2O (a) Write all of these reactions as equations. For example 1 CO +02 → CO2 can be written as 1 co +02 = CO,. (b) Order the system of equations in such a way that each equation equal 0. For example, 1 CO +02 = CO2 should be written as CO +02 - CO2 = 0. (c) Consider each chemical compound as a variable. Taking that into account, write the matrix associated to this system of equations. HINT: You should have 6 variables. (d) For this matrix, find an spanning set for the row space. (e) Remember that each of this vectors represents an equation. Write the equations that are "independent" between them. HINT: You get three at the end.
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