C10H14O + NaOH = NaC9H13 + H2O + CO2 - Chemical Equation ...

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To balance the equation C10H14O + NaOH = NaC9H13 + H2O + CO2 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 C10H14O + b NaOH = c NaC9H13 + d H2O + f CO2

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: 10a + 0b = 9c + 0d + 1f H: 14a + 1b = 13c + 2d + 0f O: 1a + 1b = 0c + 1d + 2f Na: 0a + 1b = 1c + 0d + 0f

Step 3: Solve For All Variables

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

Using Substitution or Elimination
  • 10a - 9c - 1f = 0
  • 14a + 1b - 13c - 2d = 0
  • 1a + 1b - 1d - 2f = 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:

[ 10 0 -9 0 -1 0] [ 14 1 -13 -2 0 0] [ 1 1 0 -1 -2 0] [ 0 1 -1 0 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 = 25 (C10H14O)
  • b = 26 (NaOH)
  • c = 26 (NaC9H13)
  • d = 19 (H2O)
  • f = 16 (CO2)

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.

25 C10H14O + 26 NaOH = 26 NaC9H13 + 19 H2O + 16 CO2
Reactants Products
C250250✔️
H376376✔️
O5151✔️
Na2626✔️
Since there is an equal number of each element in the reactants and products of 25C10H14O + 26NaOH = 26NaC9H13 + 19H2O + 16CO2, the equation is balanced.

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