Question

MAT-154 Topic 5 Project Worksheet Please use and submit this worksheet to complete the assignment. You may use a Microsoft Excel spreadsheet for calculations, tables, and figures and then cut and paste them into this worksheet. Student Name & Student ID: Joshua Dudley State the Chemical Reaction for your ID: Answer: C4H6O3+ H2O->C2H4O2 State the System Representation of Chemical Reaction (5 Pts.) Answer: xC4H6O3+yH2O->wC2H4O2 4X=2w 6X+2Y=4W 3X+Y=2W How many solutions do you expect the system to have? Why? (2 Pts.) Need Answer Set up the system in matrix form to be solved in MS Excel (see the many resources on internet on solving a system of linear equations using MS Excel) and solve the system using MS Excel. (3 Pts.)? Need Answer Describe an Intuitive approach to Balancing (10 Pts.) Answer: This reaction has 3 elements and 3 compounds. Carbon has 4 atoms on the left and 2 atoms on the right. Hydrogen has 8 atoms on the left and 4 atoms on the right. Oxygen has 4 atoms on the left and 2 atoms on the right. So it seems that we need to add (2)C2H4O2 on the right to balance Carbon, Hydrogen and Oxygen. State the Balanced Reaction (10 Pts.) Answer: C4H6O3+H2O->2C2H4O2 Discuss benefits of different? approaches (5 Pts.)

Answer 1

xC₄H₆O₃ + yH₂O ----> wC₂H₄O₂

4x = 2w ---------> Equation 1

6x+2y = 4w ----> Equation 2

3x+y=2w -------> Equation 3

From equation 1, w = 2x, i.e. x = w/2

Sustitute w = 2x in equation 2, then

6x + 2y = 4*2x

i.e. x = y

Therefore, x = y = w/2

i.e. The values of 'w' are 2, 4, 6, 8, 10, etc.

If w = 2, then x = y = 2/2 = 1, hence the balanced equation is C₄H₆O₃ + H₂O ----> 2C₂H₄O₂

If w = 4, then x = y = 4/2 = 2, hence the equation becomes 2C₄H₆O₃ + 2H₂O ----> 4C₂H₄O₂ but the balanced equation is the same as above, i.e. C₄H₆O₃ + H₂O ----> 2C₂H₄O₂ ​​​​​​​

If w = 6, then x = y = 6/2 = 3, hence the equation becomes 3C₄H₆O₃ + 3H₂O ----> 6C₂H₄O₂ ​​​​​​​but the balanced equation is the same as above, i.e. C₄H₆O₃ + H₂O ----> 2C₂H₄O₂ ​​​​​​​

Hence, for any value of 'w', the balanced equation is the same as C₄H₆O₃ + H₂O ----> 2C₂H₄O₂ ​​​​​​​