Answer questions using MATLAB for the scripts to perform the numerical calculations.

Consider a rocket engine burning methane (CH4) and nitrogen tetroxide (N2O4). 1. (8pts) Balance the following stoichiometric equation. Simplify the coefficients a through g to have the smallest possible integers for a and b. Do not consider any species not listed in this equation. aCH4+bN2O4cH2O+dCO2+eN2+fO2+gH2 Hint: you must use Matlab to find the coefficients. This does not mean you need to arrange the equations using Matlab. You are free (and strongly encouraged) to set up the coefficient series of equations by hand, as shown in class, and then find the numbers using the script. 2. (4pts) Find the mixture ratio for this reaction. 3. (4pts) Find the exhaust average molecular weight. 4. (4pts) Find the speed of sound of the exhaust at T=1200C if =1.4. Use R= 8314.5J/(kmolK). Hint: use the relation that g/mol is the same as kg/kmol. 5. (5pts) Find the heat of formation Qf for the reaction. Jse the standard atomic weights found in this table, and then round at the end