In an industrial metal recovery process, solid aluminum reacts with an aqueous solution of… — Armed Services Vocational Aptitude Battery (ASVAB)

In an industrial metal recovery process, solid aluminum reacts with an aqueous solution of copper(II) sulfate according to the unbalanced chemical equation:

\text{Al}(s) + \text{CuSO}_4(aq) \rightarrow \text{Al}_2(\text{SO}_4)_3(aq) + \text{Cu}(s)

When this equation is completely balanced using the smallest possible whole-number coefficients, what is the sum of all the stoichiometric coefficients?

A
$4$
B
$8$
$9$ Answer
D
$7$

Answer

The sum of all stoichiometric coefficients in the balanced equation is

9

Balancing the equation requires

2

aluminum atoms and

3

copper(II) sulfate units to react to form

1

unit of aluminum sulfate and

3

copper atoms:

2\text{Al}(s) + 3\text{CuSO}_4(aq) \rightarrow 1\text{Al}_2(\text{SO}_4)_3(aq) + 3\text{Cu}(s)

. Summing all four stoichiometric coefficients gives

2 + 3 + 1 + 3 = 9

Step-by-Step Solution

Count the number of each type of atom/polyatomic ion in the unbalanced equation.

Reactants:

1\text{ Al}

1\text{ Cu}

1\text{ SO}_4^{2-}

. Products:

2\text{ Al}

1\text{ Cu}

3\text{ SO}_4^{2-}

Establishing initial quantities identifies which species violate the Law of Conservation of Mass.

Balance the polyatomic sulfate groups by placing a coefficient of

3

before

\text{CuSO}_4

\text{Al} + 3\text{CuSO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + \text{Cu}

Treating polyatomic ions as single units when they remain intact simplifies balancing.

Balance the aluminum and copper atoms by adding coefficients of

2

\text{Al}

and

3

\text{Cu}

2\text{Al} + 3\text{CuSO}_4 \rightarrow 1\text{Al}_2(\text{SO}_4)_3 + 3\text{Cu}

Ensures equal numbers of each elemental atom on both the reactant and product sides.

Sum all lowest whole-number coefficients, including the implicit coefficient of

1

2 + 3 + 1 + 3 = 9

Calculates the total coefficient sum requested in the problem.

Key Concept

Balancing chemical equations according to the Law of Conservation of Mass using lowest whole-number stoichiometric coefficients.

Estimated Time:1m 15s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic