C6H8O4 + NaOH = NaH8O4 + C6OH - Chemical Equation Balancer

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To balance the equation C6H8O4 + NaOH = NaH8O4 + C6OH 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 represent the unknown coefficients.

a C6H8O4 + b NaOH = c NaH8O4 + d C6OH

Step 2: Create a System of Equations

Create an equation for each element (C, H, O, Na) where each term represents the number of atoms of the element in each reactant or product.

C: 6a + 0b = 0c + 6d H: 8a + 1b = 8c + 1d O: 4a + 1b = 4c + 1d Na: 0a + 1b = 1c + 0d

Step 3: Solve For All Variables

Use substitution, Gaussian elimination, or a calculator to solve for each variable.

Using Substitution or Elimination
  • 6a - 6d = 0
  • 8a + 1b - 8c - 1d = 0
  • 4a + 1b - 4c - 1d = 0
  • 1b - 1c = 0
Using Linear Systems / Algebra

Use your graphing calculator's rref() function (or an online rref calculator) to convert the following matrix into reduced row-echelon-form:

[ 6 0 0 -6 0] [ 8 1 -8 -1 0] [ 4 1 -4 -1 0] [ 0 1 -1 0 0] The resulting matrix can be used to determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients. Convert to RREF and Solve Step-by-Step

Simplify the result to get the lowest, whole integer values.

  • a = 1 (C6H8O4)
  • b = 1 (NaOH)
  • c = 1 (NaH8O4)
  • d = 1 (C6OH)

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.

C6H8O4 + NaOH = NaH8O4 + C6OH
Reactants Products
C66✔️
H99✔️
O55✔️
Na11✔️
Since there is an equal number of each element in the reactants and products of C6H8O4 + NaOH = NaH8O4 + C6OH, the equation is balanced.

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