explain to balance chemical equation by algebraic methods
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Let's try an algebraic method for
H3BO3 → H4B6O11 + H2O
It can be rather easily balanced by inspection, but let's try a more systematic approach.
What does 'balanced' mean? It means that for every element, there is the same number of atoms on both sides of the reaction equation. Our reaction has three coefficients a, b and c:
aH3BO3 → bH4B6O11 + cH2O
'Balanced' means that there is exactly the same number of atoms of each element on both sides of the equation. Using coefficients a, b and c we can tell that we have 1×a atoms of boron on the left (one atom per each H3BO3 molecule), and 6×b + 0×c on the right (6 atoms of boron per each H4B6O11 molecule and no boron in water). This gives us following equation:
1×a = 6×b + 0×c
We can write similar equations for all elements - hydrogen:
3×a = 4×b + 2×c
and oxygen:
3×a = 11×b + c
As there are no free terms in this set of equations, it has a trivial solution (a = b = c = 0) which we are not interested in. We have three equations, and three unknowns - nothing particularly difficult to solve. Quite often you will end with many more equations and many more unknows. Such equation sets is not a thing that you may want to solve manually, although when balancing chemical equations in most cases it can be done relatively easy, as most equations don't contain all unknowns. In this case we have very simple equation a = 6×b that we can use to substitute 6×b for a in the second and third equation to get:
18×b = 4×b + 2×c
18×b = 11×b + c
After some rearranging:
7×b = c
7×b = c
Both equations are identical. In algebra it usually means that the set of equations doesn't have a unique solution, but in the case of chemical equations we have one additional information - all coefficients must be integer and they must be the smallest ones. To find them we can assume one of the coefficients to be 1:
b = 1
If so
a = 6
c = 7
and indeed
6H3BO3 → H4B6O11 + 7H2O
is the balanced reaction equation.
mark as BRAINLIST
H3BO3 → H4B6O11 + H2O
It can be rather easily balanced by inspection, but let's try a more systematic approach.
What does 'balanced' mean? It means that for every element, there is the same number of atoms on both sides of the reaction equation. Our reaction has three coefficients a, b and c:
aH3BO3 → bH4B6O11 + cH2O
'Balanced' means that there is exactly the same number of atoms of each element on both sides of the equation. Using coefficients a, b and c we can tell that we have 1×a atoms of boron on the left (one atom per each H3BO3 molecule), and 6×b + 0×c on the right (6 atoms of boron per each H4B6O11 molecule and no boron in water). This gives us following equation:
1×a = 6×b + 0×c
We can write similar equations for all elements - hydrogen:
3×a = 4×b + 2×c
and oxygen:
3×a = 11×b + c
As there are no free terms in this set of equations, it has a trivial solution (a = b = c = 0) which we are not interested in. We have three equations, and three unknowns - nothing particularly difficult to solve. Quite often you will end with many more equations and many more unknows. Such equation sets is not a thing that you may want to solve manually, although when balancing chemical equations in most cases it can be done relatively easy, as most equations don't contain all unknowns. In this case we have very simple equation a = 6×b that we can use to substitute 6×b for a in the second and third equation to get:
18×b = 4×b + 2×c
18×b = 11×b + c
After some rearranging:
7×b = c
7×b = c
Both equations are identical. In algebra it usually means that the set of equations doesn't have a unique solution, but in the case of chemical equations we have one additional information - all coefficients must be integer and they must be the smallest ones. To find them we can assume one of the coefficients to be 1:
b = 1
If so
a = 6
c = 7
and indeed
6H3BO3 → H4B6O11 + 7H2O
is the balanced reaction equation.
mark as BRAINLIST
swatisharma28589:
mark as BRAINLIST
plz
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