Balance the chemical equation and create a Matrix and solve for a general solution.
KNO3 +C12H22O11→ N2 +CO2 + H2O+K2CO3
*Please Show all working out of matrices and REF
Answers
KNO3 + C12H22O11 → N2 + CO2 + H2O + K2CO3
For complicated reactions like this, your only practical option is algebra.
So assign variables to each reactant and
Product:
a KNO3 + b C12H22O11 → c N2 + d CO2 + e H2O + f K2CO3
Now write an equation for the balancing of each element:
K: a = 2f
N: a = 2c
O: 3a + 11b = 2d + e + 3f
C: 12b = d + f
H: 22b = 2e
Now you have five equations in six unknowns. Use whatever algebraic method for solving simultaneous equations you like best. Here's mine:
Substitute the value equivalent to "a" from the first equation into the third and fourth equations above:
3a + 11b = 2d + e + 3a/2
12b = d + a/2
Combine like terms in the longer equation:
3a/2 + 11b = 2d + e
Solve the shorter equation for a/2:
a/2 = 12b - d
Multiply by 3:
3a/2 = 36b - 3d
Substitute this value for 3a/2 into the previous, longer equation:
( 36b - 3d) + 11b = 2d + e
Combine like terms:
47b = 5d + e
Divide the original "H:" equation by 2:
11b = e
Substitute this value for e into the previous equation:
47b = 5d + 11b
Combine like terms:
36b = 5d
Arbitrarily set d = 1 [What d really should be will be determined later. And for that matter, alternatively b could be 1 instead and it would all work out the same in the end.]
36b = 5
b = 5/36
Start substituting d = 1 and b = 5/36 into the previous equations and solving for the other variables as you go:
11 (5/36) = e
e = 55/36
a/2 = 12(5/36) - 1
a = 4/3
4/3 = 2c
c = 2/3
4/3 = 2f
f = 2/3
So altogether one solution to the original simultaneous equations is:
a = 4/3, b = 5/36, c = 2/3, d = 1, e = 55/36, f = 2/3
These numbers balance the original chemical equation, but fractional coefficients are forbidden, so multiply all the variables by 36 to eliminate the fractions:
a = 48, b = 5, c = 24, d = 36, e = 55, f = 24
Substitute these values into the original chemical equation to see it correctly
balanced:
48 KNO3 + 5 C12H22O11 → 24 N2 + 36 CO2 + 55 H2O + 24 K2CO3