fe3o4 + hno3 = fe(no3)3 + no2 + h2o

To balance the equation Fe3O4 + HNO3 = Fe(NO3)3 + NO2 + 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.

Bạn đang xem: fe3o4 + hno3 = fe(no3)3 + no2 + h2o

a Fe3O4 + b HNO3 = c Fe(NO3)3 + d NO2 + f H2O

Step 2: Create a System of Equations

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

Fe:	3a	+	0b	=	1c	+	0d	+	0f
O:	4a	+	3b	=	9c	+	2d	+	1f
H:	0a	+	1b	=	0c	+	0d	+	2f
N:	0a	+	1b	=	3c	+	1d	+	0f

Step 3: Solve For All Variables

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

  • 3a - 1c = 0
  • 4a + 3b - 9c - 2d - 1f = 0
  • 1b - 2f = 0
  • 1b - 3c - 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:

Xem thêm: tăng trương lực cơ sinh lý

[ 3	 0	-1	 0	 0	0]
[ 4	 3	-9	-2	-1	0]
[ 0	 1	 0	 0	-2	0]
[ 0	 1	-3	-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.

Xem thêm: những thành tựu cơ bản của cuộc cách mạng công nghiệp lần thứ nhất là

  • a = 1 (Fe3O4)
  • b = 10 (HNO3)
  • c = 3 (Fe(NO3)3)
  • d = 1 (NO2)
  • f = 5 (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.

Fe3O4 + 10 HNO3 = 3 Fe(NO3)3 + NO2 + 5 H2O

Reactants Products
Fe33✔️
O3434✔️
H1010✔️
N1010✔️

Since there is an equal number of each element in the reactants and products of Fe3O4 + 10HNO3 = 3Fe(NO3)3 + NO2 + 5H2O, the equation is balanced.