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anonymous
 one year ago
Linear substitution application
anonymous
 one year ago
Linear substitution application

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I need help balancing a chemical equation (now before you send me off to the chemistry section), the way to solve it involves math: I have to balance this equation: Cu + HNO3 = Cu(NO3)2 + NO + H2O I find that the answer is 3Cu + 8HNO3 = 3Cu(NO3)2 + 2NO + 4H2O But I have no idea how to get there I found a wesite talking about using a linear substittuion, basically rewriting the equation like this a*Cu + b*HNO3 = c*Cu(NO3)2 + d*NO + e*H2O Since the same number of atoms exist on both sides, it becomes: Cu: a=c H: b=2e N: b=2c+d O: 3b=6c+d+e

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@nincompoop @phi @TheSmartOne Any help please?

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0what is the question?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0are you short an equation? b/c there are 5 unknowns

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How to solve for each unknown

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@peachpi I was thinking the same thing.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Here is where I found the technique http://www.chemicalaid.com/articles.php/view/1/howtobalancechemicalequations

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3need the matrix method to solve it???

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't have 5 equations though

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the example cleverly had enough eqautions to solve the problem.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3I arrange it as \(x_1(Cu) +x_2(HNO_3)\rightarrow x_3(Cu(NO_3)_2)+x_4(NO)+x_5(H_2O)\) Left hand side Righ hand side Cu \(x_1\) = \(x_3\) Hydrogen \(x_2\) = \(2x_5\) Nitron \(2x_2\) = \(2x_3+x_4\) Oxygen \(3x_2\) = \(6x_3+x_4+x_5\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Cu: a=c H: b=2e N: b=2c+d O: 3b=6c+d+e

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a*Cu + b*HNO3 = c*Cu(NO3)2 + d*NO + e*H2O

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Where do we go from there

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3It gives you: \(x_1x_3=0\\x_22x_5=0\\2x_22x_3x_4=0\\3x_26x_3x_4x_5=0\) hence the matrix is \[\left[\begin{matrix}1&0&1&0&0&0\\0&1&0&0&2&0\\0&2&2&1&0&0\\0&3&6&1&1&0\end{matrix}\right]\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When I do rref, I get .25 2 .25 and 3.5

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3Take row reduce echelon form, you have \(x_1=(1/4)x_5\\x_2=2x_5\\x_3=(1/4)x_5\\x_4=(7/2)x_5\) hence if \(x_5= 4\) then \(x_1= 1\\x_2=8\\x_3=1\\s_4=14\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Where did you ger that that x_1=1/4x_5

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3Now, replace all \(1(Cu) +8(HNO_3)\rightarrow 1(Cu(NO_3)_2)+14(NO)+4(H_2O)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's not correct. It's 3Cu + 8HNO3 = 3Cu(NO3)2 + 2NO + 4H2O

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3from the matrix, take row reduce echelon form, you have the first row 1 0 0 0 1/4 0 that is x1 1/4 x5 =0

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3I may make mistake at somewhere, but the technique is that. Do it carefully and you can get the answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It' in the matrix, you put for Nitrogen, 2x instead of just x

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3Yes!!!!!!!!!!! it is. My bad. I am sorry

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3then the rref is \(x_1=(3/4)x_5\\x_2= 2x_5\\x_3=(3/4)x_5\\x_4=(1/2)x_5\) if \(x_5=4\) then \(x_1=3\\x_2=8\\x_3=3\\x_4=2\) and the equation is the correct one as you had.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3Thanks for the question!! I have an opportunity to recall my knowledge. :)
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