Please help! I dont understand how the first example equation 2b-2c-d=0 was foun
ID: 3209630 • Letter: P
Question
Please help! I dont understand how the first example equation 2b-2c-d=0 was found. It doesnt make sense if the chemical equation is supposed to be balanced by the coefficients.
Thank you!
In chemistry we can use a system of linear equations to determine the coefcie a chemical equation. For example, the complete combustion of Adamantane (CioHi6 with oxygen (O2) results in carbon dioxide (CO2) and water (H2O). Because the qu each element is conserved, we must have the same quantities of carbon (C)), oxygen (O) and hydrogen (H ) on each side of the following chemical equation: a(C10H16) + b(02) c(CO2) .+ d(H2O) where the coefficients a, b, c, d are how many of each molecule is present (a) Write the equation describing the conserved quantity of each type of chemical. You wi have 3 equations in 4 unknowns The equation for conserved oxygen atoms is given as an example (b) Write the augmented matrix for this system (c) Use Gaussian elimination to find the solutions to this homogeneous system of t hree equa each tions in four unknowns. Pick the free parameter in the solution so that a, b, c, d are positive integers having no common factors. tion for complete combustion of Adamantane. This will give you the usual balancing equa- d) The chemical equation above is for the complete combustion of Adamantane and oxyge In reality, the chemical reaction involves two steps and if there is not enough oxygen rel ative to Adamantane, combustion will be incomplete. This results in the accumulation of the intermediate product carbon monoxide CO which will be created but not complet converted into carbon dioxide CO2 The incomplete combustion of octane and oxygen is described by a(C10H16) + b(02) c(CO2) + d(H2O) + e(CO) If we set a = 1 this equation becomes (C10H16) t b(02) c(CO2) + d(H2O) + e(CO) eter b Solve for c, d, e in terms of the paran (e) Note that all four unknowns must be non-negative, so that b has a specific range of possible values. Describe that range and discuss how the varying b within the range affects the output of this chemical reaction.Explanation / Answer
It is given that 'Since the quantity of each element is conserved, we must have the same quantity of oxygen on each side of the chemical reaction'
Now count the quantity of oxygen molecules on each side of the equation, we get 2b=2c+d, which gives 2b-2c-d=0.