To balance the equation (NH2)2CO + H2O = NH3 + CO2 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.
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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.
a (NH2)2CO + b H2O = c NH3 + d CO2
Step 2: Create a System of Equations
Create an equation for each element (N, H, C, O) where each term represents the number of atoms of the element in each reactant or product.
N: 2a + 0b = 1c + 0d H: 4a + 2b = 3c + 0d C: 1a + 0b = 0c + 1d O: 1a + 1b = 0c + 2d
Step 3: Solve For All Variables
Use substitution, Gaussian elimination, or a calculator đồ sộ solve for each variable.
- 2a - 1c = 0
- 4a + 2b - 3c = 0
- 1a - 1d = 0
- 1a + 1b - 2d = 0
Use your graphing calculator's rref() function (or an online rref calculator) đồ sộ convert the following matrix into reduced row-echelon-form:
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[ 2 0 -1 0 0] [ 4 2 -3 0 0] [ 1 0 0 -1 0] [ 1 1 0 -2 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.
- a = 1 ((NH2)2CO)
- b = 1 (H2O)
- c = 2 (NH3)
- d = 1 (CO2)
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.
(NH2)2CO + H2O = 2 NH3 + CO2
| N | 2 | 2 | ✔️ |
|---|---|---|---|
| H | 6 | 6 | ✔️ |
| C | 1 | 1 | ✔️ |
| O | 2 | 2 | ✔️ |
Since there is an equal number of each element in the reactants and products of (NH2)2CO + H2O = 2NH3 + CO2, the equation is balanced.
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