In 1.00 mol of potassium zirconium sulfate trihydrate, K4Zr(SO4)4 · 3 H2O, there are — Stoichiometry Chemistry Question

STEPS:

1. Analyze the Chemical Formula: Identify the components of the complex compound $K_4Zr(SO_4)_4 \cdot 3\ H_2O$ (potassium zirconium sulfate trihydrate). The subscripts and coefficients tell us the number of atoms of each element in one formula unit.
2. Understand Molar Quantities: Recall that one mole of any substance contains Avogadro's number ($6.022 \times 10^{23}$) of formula units. Therefore, in 1.00 mole of this compound, there are $6.02 \times 10^{23}$ formula units.
3. Count the Potassium (K) Atoms: In the formula, the subscript "4" attached to $K$ indicates that there are 4 potassium atoms per individual formula unit.
4. Calculate the Total Number of K Atoms: To find the total atoms in one mole of the substance, multiply the number of atoms per formula unit by the number of formula units in a mole:
$$4\ \text{atoms/unit} \times 1.00\ \text{mol} \times (6.02 \times 10^{23}\ \text{units/mol}) = \mathbf{4 \times 6.02 \times 10^{23}\ \text{potassium atoms}}$$
5. Conclusion: This calculation directly matches Option C, confirming it as the correct description of the atoms present in 1.00 mole of the compound.

WHY_OTHERS_WRONG:

• Option A ($3 \times 6.02 \times 10^{23}$ hydrogen atoms): There are 3 water molecules, each containing 2 hydrogen atoms, for a total of 6 hydrogen atoms per formula unit. Thus, there are $6 \times 6.02 \times 10^{23}$ hydrogen atoms in one mole.
• Option B ($6.02 \times 10^{23}$ sulfur atoms): The formula contains 4 sulfate groups ($(SO_4)_4$), which means there are 4 sulfur atoms per formula unit. In one mole, there would be $4 \times 6.02 \times 10^{23}$ sulfur atoms.
• Option D (4 moles of oxygen atoms): Oxygen appears in both the sulfate groups ($4 \times 4 = 16$) and the water molecules ($3 \times 1 = 3$), totaling 19 oxygen atoms per formula unit. One mole of the compound therefore contains 19 moles of oxygen atoms.
• Option E (4 moles of zirconium atoms): There is no subscript following the symbol $Zr$, which means there is only 1 zirconium atom per formula unit. One mole of the compound contains only 1 mole of zirconium atoms.