To balance the equation NaOH + CO3 = Na2CO3 + HO 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 vĩ đại represent the unknown coefficients.
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a NaOH + b CO3 = c Na2CO3 + d HO
Step 2: Create a System of Equations
Create an equation for each element (Na, O, H, C) where each term represents the number of atoms of the element in each reactant or product.
Na: 1a + 0b = 2c + 0d O: 1a + 3b = 3c + 1d H: 1a + 0b = 0c + 1d C: 0a + 1b = 1c + 0d
Step 3: Solve For All Variables
Use substitution, Gaussian elimination, or a calculator vĩ đại solve for each variable.
- 1a - 2c = 0
- 1a + 3b - 3c - 1d = 0
- 1a - 1d = 0
- 1b - 1c = 0
Use your graphing calculator's rref() function (or an online rref calculator) vĩ đại convert the following matrix into reduced row-echelon-form:
[ 1 0 -2 0 0] [ 1 3 -3 -1 0] [ 1 0 0 -1 0] [ 0 1 -1 0 0]
The resulting matrix can be used vĩ đại determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.
Simplify the result vĩ đại get the lowest, whole integer values.
- a = 2 (NaOH)
- b = 1 (CO3)
- c = 1 (Na2CO3)
- d = 2 (HO)
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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2 NaOH + CO3 = Na2CO3 + 2 HO
Since there is an equal number of each element in the reactants and products of 2NaOH + CO3 = Na2CO3 + 2HO, 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 NaOH + CO3 = Na2CO3 + HO 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 vĩ đại 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 vĩ đại balance out each element
For each element that is not equal, try vĩ đại balance it by adding more of it vĩ đại the side with less. Sometimes there may be multiple compounds with that element on one side, ví you'll need vĩ đại use your best judgement and be prepared vĩ đại go back and try the other options.
Na is not balanced. Add 1 molecule of NaOH vĩ đại the reactant (left-hand) side vĩ đại balance Sodium:
2NaOH + CO3 = Na2CO3 + HO
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Reactants Products Na 2 2 ✔️ O 5 4 ❌ H 2 1 ❌ C 1 1 ✔️
O is not balanced. Add 1 molecule of HO vĩ đại the product (right-hand) side vĩ đại balance Oxygen:
2NaOH + CO3 = Na2CO3 + 2HO
Reactants Products Na 2 2 ✔️ O 5 5 ✔️ H 2 2 ✔️ C 1 1 ✔️
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.
2NaOH + CO3 = Na2CO3 + 2HO