This one is much more difficult - you probably want to work in teams for this! C

Question

This one is much more difficult - you probably want to work in teams for this! Consider the chemical reaction C_7H_8 + HNO_3 rightarrow C_7H_5O_6N_3 + H_2O (don't try this at home folks, C_7H_5O_6N_3 is also called trinitrotoluene - TNT). Write down a system of linear equations which describe how many molecules of C_7H_8 and how many molecules of HNO_3 you need to mix together to get Z molecules of C_7H_5O_6N_3 and w molecules of water. Only write down the two equations that are obtained by asking that there be the same number of Carbon and Hydrogen atoms on both sides of the reaction (i.e. ignore the remaining two equations corresponding to conservation of Nitrogen and Oxygen atoms). Write down the system of two equations you just obtained in the second matrix form we discussed in class (not augmented matrices - the form involving matrices multiplied by vectors). Use the concept of the inverse of a matrix to solve the system for the number of molecules of C_7H_8 and HNO_3 you need, as a function of z and w

Explanation / Answer

C7H8 + HNO3 -----> C7H5O6N3 + H2O

It is not balanced one

we can balance by checking each atom

Carbons on left side = 7 ; Right side = 7

Nitrogen on left side = 1 ; Right side = 3

Hydrogen on left side = 9 ; Right side = 7

Oxygen on left side = 3 ; Right side = 7

Balanced one is

C7H8 + HNO3 -----> C7H5O6N3 + 2H2O

see carbon and hydrogen are balanced

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