Let's write the equation in the form
a Na2CO3 + b C + c N2 ---> d NaCN + e CO
where a, b, c, d, and e are unknown numbers.
Equate the left and right sides of the equation:
2 a = d for Na
a + b = d + e for C
3 a = e for O
2 c = d for N
or in matrix form
⎣⎡213001000002−1−10−10−1−10⎦⎤⋅⎣⎡abcde⎦⎤=⎣⎡00000⎦⎤ Then using Gauss-Jordan method
⎣⎡213001000002−1−10−10−1−10⎦⎤→⎣⎡113001000002−1/2−10−10−1−10⎦⎤→⎣⎡100001000002−1/2−1/23/2−10−1−10⎦⎤→
⎣⎡100001000002−1/2−1/23/2−10−1−10⎦⎤→⎣⎡100001000020−1/2−1/2−13/20−10−1⎦⎤→⎣⎡100001000010−1/2−1/2−1/23/20−10−1⎦⎤→
⎣⎡100001000010−1/2−1/2−1/210−10−2/3⎦⎤→⎣⎡1000010000100001−1/3−4/3−1/3−2/3⎦⎤
Therefore if e = 3 then a = 1, b = 4, c =1, d = 2 and the equation is
Na2CO3 + 4C + N2 ---> 2NaCN + 3CO
Comments