ca + n2

To balance the equation Ca + N2 = Ca3N2 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 Ca + b N2 = c Ca3N2

Step 2: Create a System of Equations

Create an equation for each element (Ca, N) where each term represents the number of atoms of the element in each reactant or product.

Ca:	1a	+	0b	=	3c
N:	0a	+	2b	=	2c

Step 3: Solve For All Variables

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

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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[ 1	 0	-3	0]
[ 0	 2	-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 = 3 (Ca)
  • b = 1 (N2)
  • c = 1 (Ca3N2)

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.

3 Ca + N2 = Ca3N2

Reactants Products
Ca33✔️
N22✔️

Since there is an equal number of each element in the reactants and products of 3Ca + N2 = Ca3N2, the equation is balanced.