C3H4 + AgNO3 + NH3 = C3Ag4 + NH4NO3 - Chemical Equation Balancer

To balance the equation C3H4 + AgNO3 + NH3 = C3Ag4 + NH4NO3 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 tướng represent the unknown coefficients.

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a C₃H₄ + b AgNO₃ + c NH₃ = d C₃Ag₄ + f NH₄NO₃

Step 2: Create a System of Equations

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

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

Step 3: Solve For All Variables

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

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

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

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

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

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

a = 1 (C3H4)
b = 4 (AgNO3)
c = 4 (NH3)
d = 1 (C3Ag4)
f = 4 (NH4NO3)

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.

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C₃H₄ + 4 AgNO₃ + 4 NH₃ = C₃Ag₄ + 4 NH₄NO₃

	Reactants	Products
C	3	3	✔️
H	16	16	✔️
Ag	4	4	✔️
N	8	8	✔️
O	12	12	✔️

Since there is an equal number of each element in the reactants and products of C3H4 + 4AgNO3 + 4NH3 = C3Ag4 + 4NH4NO3, the equation is balanced.

The law of conservation of mass states that matter cannot be created or destroyed, which means there must be the same number atoms at the over of a chemical reaction as at the beginning. To be balanced, every element in C3H4 + AgNO3 + NH3 = C3Ag4 + NH4NO3 must have the same number of atoms on each side of the equation. When using the inspection method (also known as the trial-and-error method), this principle is used to tướng balance one element at a time until both sides are equal and the chemical equation is balanced.

Step 1: Count the number of each element on the left and right hand sides

	Reactants (Left Hand Side)				Products (Right Hand Side)
	Reactants	Products
	C₃H₄	AgNO₃	NH₃	Total	C₃Ag₄	NH₄NO₃	Total
C	3			3	3		3	✔️
H	4		3	7		4	4	❌
Ag		1		1	4		4	❌
N		1	1	2		2	2	✔️
O		3		3		3	3	✔️

Step 2: Multiply coefficients for compounds to tướng balance out each element

For each element that is not equal, try to tướng balance it by adding more of it to tướng the side with less. Sometimes there may be multiple compounds with that element on one side, ví you'll need to tướng use your best judgement and be prepared to tướng go back and try the other options.

Ag is not balanced. Add 3 molecules of AgNO₃ to tướng the reactant (left-hand) side to tướng balance Silver:
C₃H₄ + 4AgNO₃ + NH₃ = C₃Ag₄ + NH₄NO₃
Reactants Products
C 3 3 ✔️
H 7 4 ❌
Ag 4 4 ✔️
N 5 2 ❌
O 12 3 ❌
O is not balanced. Add 3 molecules of NH₄NO₃ to tướng the product (right-hand) side to tướng balance Oxygen:
C₃H₄ + 4AgNO₃ + NH₃ = C₃Ag₄ + 4NH₄NO₃
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Reactants Products
C 3 3 ✔️
H 7 16 ❌
Ag 4 4 ✔️
N 5 8 ❌
O 12 12 ✔️
H is not balanced. Add 3 molecules of NH₃ to tướng the reactant (left-hand) side to tướng balance Hydrogen:
C₃H₄ + 4AgNO₃ + 4NH₃ = C₃Ag₄ + 4NH₄NO₃
Reactants Products
C 3 3 ✔️
H 16 16 ✔️
Ag 4 4 ✔️
N 8 8 ✔️
O 12 12 ✔️