To balance the equation C6H5OH + Br2 = C6H2Br3OH + HBr 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 vĩ đại represent the unknown coefficients.
a C6H5OH + b Br2 = c C6H2Br3OH + d HBr
Step 2: Create a System of Equations
Create an equation for each element (C, H, O, Br) where each term represents the number of atoms of the element in each reactant or product.
C: 6a + 0b = 6c + 0d H: 6a + 0b = 3c + 1d O: 1a + 0b = 1c + 0d Br: 0a + 2b = 3c + 1d
Step 3: Solve For All Variables
Use substitution, Gaussian elimination, or a calculator vĩ đại solve for each variable.
- 6a - 6c = 0
- 6a - 3c - 1d = 0
- 1a - 1c = 0
- 2b - 3c - 1d = 0
Use your graphing calculator's rref() function (or an online rref calculator) vĩ đại convert the following matrix into reduced row-echelon-form:
Xem thêm: c2h2 ra ch2=ch cl
[ 6 0 -6 0 0] [ 6 0 -3 -1 0] [ 1 0 -1 0 0] [ 0 2 -3 -1 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 = 1 (C6H5OH)
- b = 3 (Br2)
- c = 1 (C6H2Br3OH)
- d = 3 (HBr)
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.
C6H5OH + 3 Br2 = C6H2Br3OH + 3 HBr
Since there is an equal number of each element in the reactants and products of C6H5OH + 3Br2 = C6H2Br3OH + 3HBr, the equation is balanced.
Xem thêm: zn(oh)2 + hcl