To balance the equation C2H5OH + O2 = CH3CHO + H2O 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 đồ sộ represent the unknown coefficients.
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a C2H5OH + b O2 = c CH3CHO + d H2O
Step 2: Create a System of Equations
Create an equation for each element (C, H, O) where each term represents the number of atoms of the element in each reactant or product.
C: 2a + 0b = 2c + 0d H: 6a + 0b = 4c + 2d O: 1a + 2b = 1c + 1d
Step 3: Solve For All Variables
Use substitution, Gaussian elimination, or a calculator đồ sộ solve for each variable.
- 2a - 2c = 0
- 6a - 4c - 2d = 0
- 1a + 2b - 1c - 1d = 0
Use your graphing calculator's rref() function (or an online rref calculator) đồ sộ convert the following matrix into reduced row-echelon-form:
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[ 2 0 -2 0 0] [ 6 0 -4 -2 0] [ 1 2 -1 -1 0]
The resulting matrix can be used đồ sộ determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.
Simplify the result đồ sộ get the lowest, whole integer values.
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- a = 2 (C2H5OH)
- b = 1 (O2)
- c = 2 (CH3CHO)
- d = 2 (H2O)
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.
2 C2H5OH + O2 = 2 CH3CHO + 2 H2O
Since there is an equal number of each element in the reactants and products of 2C2H5OH + O2 = 2CH3CHO + 2H2O, the equation is balanced.