In a submarine life-support system, carbon dioxide (CO_2) is scrubbed from the cabin atmos… — Armed Services Vocational Aptitude Battery (ASVAB)

In a submarine life-support system, carbon dioxide ( $CO_2$ ) is scrubbed from the cabin atmosphere by reacting with solid lithium hydroxide ( $LiOH$ ) to produce solid lithium carbonate ( $Li_2CO_3$ ) and water vapor ( $H_2O$ ). Which of the following represents the correctly balanced chemical equation for this reaction?

A
$LiOH + CO_2 \rightarrow Li_2CO_3 + H_2O$
$2LiOH + CO_2 \rightarrow Li_2CO_3 + H_2O$ Answer
C
$Li_2OH + CO_2 \rightarrow Li_2CO_3 + H_2O$
D
$LiOH + CO_2 \rightarrow LiCO_2 + H_2O$

Answer

The balanced chemical equation is

2LiOH + CO_2 \rightarrow Li_2CO_3 + H_2O

Placing a coefficient of 2 in front of lithium hydroxide yields equal quantities of each element on both sides: 2 lithium atoms, 1 carbon atom, 4 oxygen atoms, and 2 hydrogen atoms, satisfying the law of conservation of mass.

Step-by-Step Solution

Write the unbalanced skeleton equation using the correct chemical formulas for all reactants and products.

LiOH + CO_2 \rightarrow Li_2CO_3 + H_2O

Establishing the correct formulas ensures that the identities of the chemical substances are maintained.

Count the number of each type of atom on both sides of the equation.

Reactants: 1 Li, 1 C, 3 O, 1 H. Products: 2 Li, 1 C, 4 O, 2 H.

An atom inventory reveals which elements violate the law of conservation of mass.

Place a coefficient of 2 in front of

LiOH

on the reactant side to balance the lithium and hydrogen atoms.

2LiOH + CO_2 \rightarrow Li_2CO_3 + H_2O

Using whole-number coefficients balances atoms without altering compound identities.

Re-verify the atom count for every element across the entire equation.

Reactants: 2 Li, 1 C, 4 O, 2 H. Products: 2 Li, 1 C, 4 O, 2 H.

Confirming equal atom counts ensures the equation satisfies the law of conservation of mass.

Key Concept

Balancing chemical equations by adding stoichiometric coefficients while keeping chemical formulas unchanged.

Estimated Time:1m 30s

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