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
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)|
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
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 ✔️
Step 3: Verify that the equation is balanced
Since there are an equal number of atoms of each element on both sides, the equation is balanced.
C3H4 + 4AgNO3 + 4NH3 = C3Ag4 + 4NH4NO3