To balance the equation C6H6 + H2 = C6H12 using the algebraic method step-by-step, you must have experience solving systems of linear equations. The most common methods are substitution/elimination and linear algebra, but any similar method will work.
Step 1: Label Each Compound With a Variable
Label each compound (reactant or product) in the equation with a variable to tướng represent the unknown coefficients.
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a C6H6 + b H2 = c C6H12
Step 2: Create a System of Equations
Create an equation for each element (C, H) where each term represents the number of atoms of the element in each reactant or product.
C: 6a + 0b = 6c H: 6a + 2b = 12c
Step 3: Solve For All Variables
Use substitution, Gaussian elimination, or a calculator to tướng solve for each variable.
- 6a - 6c = 0
- 6a + 2b - 12c = 0
Use your graphing calculator's rref() function (or an online rref calculator) to tướng convert the following matrix into reduced row-echelon-form:
Xem thêm: hcl ra agcl
[ 6 0 -6 0] [ 6 2 -12 0]
The resulting matrix can be used to tướng determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.
Simplify the result to tướng get the lowest, whole integer values.
Xem thêm: trong quá trình thực hiện thuật toán, khi nào cần dùng cấu trúc rẽ nhánh?
- a = 1 (C6H6)
- b = 3 (H2)
- c = 1 (C6H12)
Step 4: Substitute Coefficients and Verify Result
Count the number of atoms of each element on each side of the equation and verify that all elements and electrons (if there are charges/ions) are balanced.
C6H6 + 3 H2 = C6H12
| C | 6 | 6 | ✔️ |
|---|---|---|---|
| H | 12 | 12 | ✔️ |
Since there is an equal number of each element in the reactants and products of C6H6 + 3H2 = C6H12, the equation is balanced.
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