Ag + HNO3 = AgNO3 + NO2 + H2O - Chemical Equation Balancer

To balance the equation Ag + HNO3 = AgNO3 + 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 lớn represent the unknown coefficients.

Bạn đang xem: hno3 +ag

a Ag + b HNO₃ = c AgNO₃ + d NO₂ + f H₂O

Step 2: Create a System of Equations

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

Ag:	1a	+	0b	=	1c	+	0d	+	0f
H:	0a	+	1b	=	0c	+	0d	+	2f
N:	0a	+	1b	=	1c	+	1d	+	0f
O:	0a	+	3b	=	3c	+	2d	+	1f

Step 3: Solve For All Variables

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

1a - 1c = 0
1b - 2f = 0
1b - 1c - 1d = 0
3b - 3c - 2d - 1f = 0

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

Xem thêm: giải bài tập toán 10 cánh diều

[ 1	 0	-1	 0	 0	0]
[ 0	 1	 0	 0	-2	0]
[ 0	 1	-1	-1	 0	0]
[ 0	 3	-3	-2	-1	0]

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

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

Xem thêm: hãy chỉ ra một số nguyên tố lớn hơn 40 và nhỏ hơn 50

a = 1 (Ag)
b = 2 (HNO3)
c = 1 (AgNO3)
d = 1 (NO2)
f = 1 (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.

Ag + 2 HNO₃ = AgNO₃ + NO₂ + H₂O