In one molecule of ammonium sulfate, (NH4)2SO4, how many individual atoms (of all elements combined) are present in total?

Introduction / Context:
Counting the total number of atoms in a chemical formula is a basic but important skill in chemistry. It helps with understanding stoichiometry, molar mass calculations, and balancing equations. Ammonium sulfate, written as (NH4)2SO4, contains multiple types of atoms grouped in polyatomic ions. This question asks you to carefully unpack the formula and determine how many atoms in total are present in one molecule of this compound.

Given Data / Assumptions:

• The compound is ammonium sulfate with formula (NH4)2SO4.
• We need the total count of all atoms: nitrogen, hydrogen, sulfur, and oxygen.
• The subscript outside the bracket multiplies everything inside the bracket.
• We assume the formula is correctly written and represents one neutral molecule.

Concept / Approach:
To count atoms in a formula like (NH4)2SO4, we expand it by distributing the outside subscript over the inner group. The group NH4 appears twice, so each atom inside it is multiplied by 2. Then we add the atoms from the sulfate part, SO4. Finally, we sum all atoms of each element to get the total number of atoms in a single formula unit. This is straightforward but requires careful attention to subscripts and brackets.

Step-by-Step Solution:
Step 1: Expand the ammonium part, (NH4)2. Inside NH4 there is 1 nitrogen and 4 hydrogens. Because of the outside subscript 2, we have: N = 1 * 2 = 2 nitrogen atoms, H = 4 * 2 = 8 hydrogen atoms. Step 2: Identify atoms in the sulfate part, SO4. SO4 has 1 sulfur and 4 oxygen atoms. Step 3: Add up atoms of each element. Nitrogen: 2 Hydrogen: 8 Sulfur: 1 Oxygen: 4 Step 4: Compute the total number of atoms. Total atoms = 2 + 8 + 1 + 4 = 15.

Verification / Alternative check:
We can double check by rewriting the formula without brackets: (NH4)2SO4 = N2H8SO4. Now it is easy to see that there are 2 nitrogen atoms, 8 hydrogen atoms, 1 sulfur atom, and 4 oxygen atoms. Summing these gives 2 + 8 + 1 + 4 = 15 atoms. This independent way of writing the formula confirms the earlier counting method. If any step gave a different total, it would indicate a misreading of subscripts or brackets, but here both methods agree on 15 atoms.

Why Other Options Are Wrong:
Option B (14): This would mean you have missed one atom somewhere, likely by forgetting that the NH4 group is doubled. Option C (13): This would require multiple counting mistakes, such as ignoring both the bracket and some atoms. Option D (12): This is far too low and would correspond to misreading the formula as something like NH4SO4 without doubling the ammonium group.

Common Pitfalls:
Students often forget to multiply all atoms inside a bracket by the subscript outside the bracket. Another common error is miscounting hydrogen atoms, especially when many are present. To avoid this, always expand bracketed groups first and write intermediate results clearly, as in N2H8SO4. Practising with a few similar formulas, such as (NH4)2CO3 or Ca(NO3)2, quickly builds confidence in correctly counting atoms in compounds containing polyatomic ions.

Final Answer:
One molecule of (NH4)2SO4 contains a total of 15 atoms.