MnO₂ + x HCl → MnCl₂ + y H₂O + z Cl₂

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Feb 15, 2024

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In order to balance the above chemical equation, the values of x, y and z respectively are :

a) 6, 2, 2

b) 4, 1, 2

c) 4, 2, 1

d) 2, 2, 1

Manganese(IV) oxide + x Hydrochloric acid = Manganese(II) chloride + y Water + z Chlorine

MnO₂ + x HCl → MnCl₂ + y H₂O + z Cl₂

This shows a chemical equation between manganese dioxide (MnO₂) and hydrochloric acid (HCl) to produce manganese chloride (MnCl₂), water (H₂O), and chlorine gas (Cl₂). To balance the equation, you need to make sure that there are the same number of atoms of each element on both sides of the equation.

Balancing step by step using the inspection method
Let’s balance this equation using the inspection method. First, we set all coefficients to 1: 1 MnO₂ + 1 HCl = 1 MnCl₂ + 1 H₂O + 1 Cl₂ For each element, we check if the number of atoms is balanced on both sides of the equation. Mn is balanced: 1 atom in reagents and 1 atom in products. O is not balanced: 2 atoms in reagents and 1 atom in products. In order to balance O on both sides we: Multiply coefficient of H₂O with 2 1 MnO₂ + 1 HCl = 1 MnCl₂ + 2 H₂O + 1 Cl₂ H is not balanced: 1 atom in reagents and 4 atoms in products. In order to balance H on both sides we: Multiply coefficient of HCl with 4 1 MnO₂ + 4 HCl = 1 MnCl₂ + 2 H₂O + 1 Cl₂ Cl is balanced: 4 atoms in reagents and 4 atoms in products. All atoms are now balanced and the whole equation is fully balanced: MnO₂ + 4 HCl = MnCl₂ + 2 H₂O + 1 Cl₂ the correct option is c) 4, 2, 1

Balancing step by step using the inspection method

Let’s balance this equation using the inspection method.

First, we set all coefficients to 1:

1 MnO₂ + 1 HCl = 1 MnCl₂ + 1 H₂O + 1 Cl₂

For each element, we check if the number of atoms is balanced on both sides of the equation.

Mn is balanced: 1 atom in reagents and 1 atom in products.

O is not balanced: 2 atoms in reagents and 1 atom in products.

In order to balance O on both sides we:
Multiply coefficient of H₂O with 2
1 MnO₂ + 1 HCl = 1 MnCl₂ + 2 H₂O + 1 Cl₂

H is not balanced: 1 atom in reagents and 4 atoms in products.

In order to balance H on both sides we:
Multiply coefficient of HCl with 4
1 MnO₂ + 4 HCl = 1 MnCl₂ + 2 H₂O + 1 Cl₂

Cl is balanced: 4 atoms in reagents and 4 atoms in products.

All atoms are now balanced and the whole equation is fully balanced:
MnO₂ + 4 HCl = MnCl₂ + 2 H₂O + 1 Cl₂

the correct option is c) 4, 2, 1

Balancing step by step using the algebraic method
Let’s balance this equation using the algebraic method. First, we set all coefficients to variables a, b, c, d, … a MnO₂ + b HCl = c MnCl₂ + d H₂O + e Cl₂ Now we write down algebraic equations to balance of each atom: Mn: a * 1 = c * 1 O: a * 2 = d * 1 H: b * 1 = d * 2 Cl: b * 1 = c * 2 + e * 2 Now we assign a=1 and solve the system of linear algebra equations: a = c a * 2 = d b = d * 2 b = c * 2 + e * 2 a = 1 Solving this linear algebra system we arrive at: a = 1 b = 4 c = 1 d = 2 e = 1 To get to integer coefficients we multiply all variable by 1 a = 1 b = 4 c = 1 d = 2 e = 1 Now we substitute the variables in the original equations with the values obtained by solving the linear algebra system and arrive at the fully balanced equation: MnO₂ + 4 HCl = MnCl₂ + 2 H₂O + 1 Cl₂ the correct option is c) 4, 2, 1

Balancing step by step using the algebraic method

Let’s balance this equation using the algebraic method.

First, we set all coefficients to variables a, b, c, d, …
a MnO₂ + b HCl = c MnCl₂ + d H₂O + e Cl₂

Now we write down algebraic equations to balance of each atom:
Mn: a * 1 = c * 1
O: a * 2 = d * 1
H: b * 1 = d * 2
Cl: b * 1 = c * 2 + e * 2

Now we assign a=1 and solve the system of linear algebra equations:
a = c
a * 2 = d
b = d * 2
b = c * 2 + e * 2
a = 1

Solving this linear algebra system we arrive at:
a = 1
b = 4
c = 1
d = 2
e = 1

To get to integer coefficients we multiply all variable by 1
a = 1
b = 4
c = 1
d = 2
e = 1

Now we substitute the variables in the original equations with the values obtained by solving the linear algebra system and arrive at the fully balanced equation:

MnO₂ + 4 HCl = MnCl₂ + 2 H₂O + 1 Cl₂

the correct option is c) 4, 2, 1

Manganese(IV) oxide + 4 Hydrochloric acid = Manganese(II) chloride + 2 Water + Chlorine

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