# mg +hcl

To balance the equation Mg + HCl = MgCl2 + H2 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 lớn represent the unknown coefficients.

a Mg + b HCl = c MgCl2 + d H2

### Step 2: Create a System of Equations

Create an equation for each element (Mg, H, Cl) where each term represents the number of atoms of the element in each reactant or product.

Mg: 1a + 0b = 1c + 0d H: 0a + 1b = 0c + 2d Cl: 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
• 1b - 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:

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[ 1 0 -1 0 0] [ 0 1 0 -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.

• a = 1 (Mg)
• b = 2 (HCl)
• c = 1 (MgCl2)
• d = 1 (H2)

### 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.

Mg + 2 HCl = MgCl2 + H2

Reactants Products Mg 1 1 ✔️ 2 2 ✔️ 2 2 ✔️

Since there is an equal number of each element in the reactants and products of Mg + 2HCl = MgCl2 + H2, the equation is balanced.

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