co2 c6h5ona

To balance the equation C6H5ONa + CO2 + H2O = C6H5OH + Na2CO3 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 tát represent the unknown coefficients.

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a C6H5ONa + b CO2 + c H2O = d C6H5OH + f Na2CO3

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	+	1b	+	0c	=	6d	+	1f
H:	5a	+	0b	+	2c	=	6d	+	0f
O:	1a	+	2b	+	1c	=	1d	+	3f
Na:	1a	+	0b	+	0c	=	0d	+	2f

Step 3: Solve For All Variables

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

  • 6a + 1b - 6d - 1f = 0
  • 5a + 2c - 6d = 0
  • 1a + 2b + 1c - 1d - 3f = 0
  • 1a - 2f = 0

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

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[ 6	 1	 0	-6	-1	0]
[ 5	 0	 2	-6	 0	0]
[ 1	 2	 1	-1	-3	0]
[ 1	 0	 0	 0	-2	0]

The resulting matrix can be used to tát determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.

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

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  • a = 2 (C6H5ONa)
  • b = 1 (CO2)
  • c = 1 (H2O)
  • d = 2 (C6H5OH)
  • f = 1 (Na2CO3)

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 C6H5ONa + CO2 + H2O = 2 C6H5OH + Na2CO3

Reactants Products
C1313✔️
H1212✔️
O55✔️
Na22✔️

Since there is an equal number of each element in the reactants and products of 2C6H5ONa + CO2 + H2O = 2C6H5OH + Na2CO3, the equation is balanced.