To balance the equation CH3COOC6H5 + KOH = C6H5OK + CH3COOK + 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 CH3COOC6H5 + b KOH = c C6H5OK + d CH3COOK + f H2O
Step 2: Create a System of Equations
Create an equation for each element (C, H, O, K) where each term represents the number of atoms of the element in each reactant or product.
C: 8a + 0b = 6c + 2d + 0f H: 8a + 1b = 5c + 3d + 2f O: 2a + 1b = 1c + 2d + 1f K: 0a + 1b = 1c + 1d + 0f
Step 3: Solve For All Variables
Use substitution, Gaussian elimination, or a calculator đồ sộ solve for each variable.
- 8a - 6c - 2d = 0
- 8a + 1b - 5c - 3d - 2f = 0
- 2a + 1b - 1c - 2d - 1f = 0
- 1b - 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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[ 8 0 -6 -2 0 0] [ 8 1 -5 -3 -2 0] [ 2 1 -1 -2 -1 0] [ 0 1 -1 -1 0 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.
- a = 1 (CH3COOC6H5)
- b = 2 (KOH)
- c = 1 (C6H5OK)
- d = 1 (CH3COOK)
- f = 1 (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.
CH3COOC6H5 + 2 KOH = C6H5OK + CH3COOK + H2O
Since there is an equal number of each element in the reactants and products of CH3COOC6H5 + 2KOH = C6H5OK + CH3COOK + H2O, the equation is balanced.