Which one of the following is the correct molecular formula of ammonium carbonate if the valency of ammonium ion is (+1) and carbonate anion is (-2)?

Question

Prepp Team · Accepted Answer

Understanding Ammonium Carbonate Molecular Formula

To determine the correct molecular formula for an ionic compound like ammonium carbonate, we need to consider the charges (valencies) of the individual ions involved. The formula must represent a neutral compound, meaning the total positive charge from the cations must balance the total negative charge from the anions.

Identifying the Ions and Their Valencies

The question provides the necessary information:

The cation is the ammonium ion, which has a valency (charge) of +1. Its chemical formula is given as \(\text{NH}_4^+\).
The anion is the carbonate ion, which has a valency (charge) of -2. Its chemical formula is \(\text{CO}_3^{2-}\).

Balancing Charges to Find the Formula

We need to find the smallest whole number ratio of ammonium ions to carbonate ions that results in a net charge of zero. We can use the criss-cross method or simply balance the charges:

Each ammonium ion (\(\text{NH}_4^+\)) carries a +1 charge.
Each carbonate ion (\(\text{CO}_3^{2-}\)) carries a -2 charge.

To balance the -2 charge of one carbonate ion, we need enough ammonium ions to contribute a total charge of +2. Since each ammonium ion contributes +1, we need two ammonium ions (\(2 \times +1 = +2\)).

So, the ratio of ammonium ions to carbonate ions is 2:1.

When writing the formula, the cation (\(\text{NH}_4\)) comes first, followed by the anion (\(\text{CO}_3\)). The number of each ion needed becomes the subscript for the other ion (ignoring the signs of the charges).

The valency of \(\text{NH}_4^+\) is 1. This becomes the subscript for \(\text{CO}_3\). (Subscript 1 is usually omitted).
The valency of \(\text{CO}_3^{2-}\) is 2. This becomes the subscript for \(\text{NH}_4\). Since \(\text{NH}_4\) is a polyatomic ion, we enclose it in parentheses before adding the subscript 2.

Following this method:

Write the ions with their charges: \(\text{NH}_4^{1+}\) \(\text{CO}_3^{2-}\)

Criss-cross the magnitudes of the charges as subscripts:

\(\text{(NH}_4\text{)}_2 \text{(CO}_3\text{)}_1\)

Omitting the subscript 1 and parentheses where not needed for a single polyatomic ion, the formula becomes:

\(\text{(NH}_4\text{)}_2\text{CO}_3\)

Comparing with Options

Let's look at the given options:

Option	Formula	Analysis
1	\(\text{(NH}_4\text{)}_2\text{CO}_3\)	Matches our derived formula. Two \(\text{NH}_4^+\) ions (\(2 \times +1 = +2\)) balance one \(\text{CO}_3^{2-}\) ion (\(-2\)). Net charge is \(+2 - 2 = 0\). This is the correct molecular formula of ammonium carbonate.
2	\(\text{NH}_4\text{(CO}_3\text{)}_2\)	This suggests one \(\text{NH}_4^+\) ion (\(+1\)) and two \(\text{CO}_3^{2-}\) ions (\(2 \times -2 = -4\)). Net charge is \(+1 - 4 = -3\), which is not neutral. Incorrect formula for ammonium carbonate.
3	\(\text{(NH}_3\text{)}_2\text{CO}_3\)	This formula uses \(\text{NH}_3\) (ammonia) instead of \(\text{NH}_4\) (ammonium ion). Ammonia is a neutral molecule, not an ion. This is an incorrect representation for ammonium carbonate.
4	\(\text{NH}_4\text{CO}_3\)	This suggests one \(\text{NH}_4^+\) ion (\(+1\)) and one \(\text{CO}_3^{2-}\) ion (\(-2\)). Net charge is \(+1 - 2 = -1\), which is not neutral. Incorrect formula for ammonium carbonate.

Based on the charge balancing and comparison with the options, the correct molecular formula for ammonium carbonate is \(\text{(NH}_4\text{)}_2\text{CO}_3\).

The correct option is 1: \(\text{(NH}_4\text{)}_2\text{CO}_3\).

Revision Table: Ammonium Carbonate Formula

Concept	Description	Application to Ammonium Carbonate
Ionic Compound	Formed between cations (positive ions) and anions (negative ions).	Ammonium carbonate is an ionic compound formed from ammonium cation and carbonate anion.
Valency (Charge)	The combining capacity of an element or ion; the charge it carries.	Ammonium ion has valency +1, carbonate ion has valency -2.
Neutral Compound	The total positive charge equals the total negative charge, resulting in a net charge of zero.	The formula \(\text{(NH}_4\text{)}_2\text{CO}_3\) has a total positive charge of \(2 \times (+1) = +2\) and a total negative charge of \(-2\), resulting in a net charge of 0.
Criss-Cross Method	A way to determine the formula of an ionic compound by swapping the magnitudes of the charges as subscripts.	Valency 1 from \(\text{NH}_4^+\) goes to \(\text{CO}_3\); Valency 2 from \(\text{CO}_3^{2-}\) goes to \(\text{NH}_4\). This yields \(\text{(NH}_4\text{)}_2\text{CO}_3\).

Additional Information: Ionic Compound Formulas

When writing the molecular formula for any ionic compound, follow these general steps:

Identify the cation (positive ion) and anion (negative ion) involved.
Write the symbol of the cation first, followed by the symbol of the anion.
Determine the charge (valency) of each ion.
Use the criss-cross method: The magnitude of the cation's charge becomes the subscript for the anion, and the magnitude of the anion's charge becomes the subscript for the cation.
If a polyatomic ion (like ammonium, sulfate, carbonate, nitrate) requires a subscript greater than 1, enclose the polyatomic ion in parentheses before writing the subscript.
Simplify the subscripts to the lowest whole number ratio, if necessary (though in this case, 2:1 is already the lowest ratio).
Omit any subscript of 1.

For example, the formula for sodium chloride (\(\text{Na}^+\), \(\text{Cl}^-\)) is \(\text{NaCl}\) (\(1:1\) ratio). The formula for magnesium chloride (\(\text{Mg}^{2+}\), \(\text{Cl}^-\)) is \(\text{MgCl}_2\) (\(1:2\) ratio). The formula for aluminum oxide (\(\text{Al}^{3+}\), \(\text{O}^{2-}\)) is \(\text{Al}_2\text{O}_3\) (\(2:3\) ratio).