To balance the equation CaC2 + H2O = Ca(OH)2 + C2H2 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.
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a CaC2 + b H2O = c Ca(OH)2 + d C2H2
Step 2: Create a System of Equations
Create an equation for each element (Ca, C, H, O) where each term represents the number of atoms of the element in each reactant or product.
Ca: 1a + 0b = 1c + 0d C: 2a + 0b = 0c + 2d H: 0a + 2b = 2c + 2d O: 0a + 1b = 2c + 0d
Step 3: Solve For All Variables
Use substitution, Gaussian elimination, or a calculator lớn solve for each variable.
- 1a - 1c = 0
- 2a - 2d = 0
- 2b - 2c - 2d = 0
- 1b - 2c = 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: lớp 10b có 28 học sinh
[ 1 0 -1 0 0] [ 2 0 0 -2 0] [ 0 2 -2 -2 0] [ 0 1 -2 0 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: bài 28 địa 10 chân trời sáng tạo
- a = 1 (CaC2)
- b = 2 (H2O)
- c = 1 (Ca(OH)2)
- d = 1 (C2H2)
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.
CaC2 + 2 H2O = Ca(OH)2 + C2H2
| Ca | 1 | 1 | ✔️ |
|---|---|---|---|
| C | 2 | 2 | ✔️ |
| H | 4 | 4 | ✔️ |
| O | 2 | 2 | ✔️ |
Since there is an equal number of each element in the reactants and products of CaC2 + 2H2O = Ca(OH)2 + C2H2, the equation is balanced.
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