I have a college assignment where I must balance the following equation :
NaOH + H2S04 --> Na2S04 + H20
my knowledge of python and coding in general is extremely limited at the moment. So far I have attempted to use matrices to solve the equation. It looks like I am getting the solution a=b=x=y=0 I guess I need to set one of the variables to 1 and solve for the other three. I'm not sure how to go about doing this, I have had a search, it looks like other people have used more sophisticated code and I'm not really able to follow it!
here's what I have so far
#aNaOH + bH2S04 --> xNa2SO4 +y H20
#Na: a=2x
#O: a+4b=4x+y
#H: a+2h = 2y
#S: b = x
#a+0b -2x+0y = 0
#a+4b-4x-y=0
#a+2b+0x-2y=0
#0a +b-x+0y=0
A=array([[1,0,-2,0],
[1,4,-4,-1],
[1,2,0,-2],
[0,1,-1,0]])
b=array([0,0,0,0])
c =linalg.solve(A,b)
print c
0.0.0.0
The problem is that you have constructed a linear system with b being a zero-vector. Now for such system there is always the straight-forward answer that all variables are zeros as well. Since multiplying a number with zero and adding zeros up results always in zeros.
A solution might be to assign 1 to a variable. Take for instance a. If we assign a = 1, then we will get b, x and y in function of a being 1.
So now or linear system is:
B X Y | #
2 |1 # A = 2X
-4 4 1 |1 # A+4B = 4X+4Y
-2 2 |1 # A+2B = 2Y
-1 1 0 |0 # B = X
Or putting it into code:
>>> A = array([[0,2,0],[-4,4,1],[-2,0,2],[-1,1,0]])
>>> B = array([1,1,1,0])
>>> linalg.lstsq(A,B)
(array([ 0.5, 0.5, 1. ]), 6.9333477997940491e-33, 3, array([ 6.32979642, 2.5028631 , 0.81814033]))
So that means that:
A = 1, B = 0.5, X = 0.5, Y = 1.
If we multiply this by 2, we get:
2 NaOH + H2S04 -> Na2S04 + 2 H20
Which is correct.