Question

A sample of ammonium phosphate, \(\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4}\), contains 6 moles of hydrogen atoms. The number of moles of oxygen atoms in the sample is: (a) 1 (b) 2 (c) 4 (d) 6

Short answer

The number of moles of oxygen atoms in the sample is 2.

Step-by-step solution

Identify the chemical formula

Examine the chemical formula of ammonium phosphate, which is \(\left(\mathrm{NH}_{4}\right)_{3}\mathrm{PO}_{4}\).

Calculate the moles of hydrogen in the formula

Calculate the total number of moles of hydrogen atoms in the chemical formula. In ammonium phosphate, every ammonium ion \(\mathrm{NH}_{4}^{+}\) has 4 hydrogen atoms and there are 3 ammonium ions, giving a total of 3 * 4 = 12 hydrogen atoms in the formula.

Relate the moles of hydrogen to the sample

Since the sample contains 6 moles of hydrogen atoms and the formula has 12 hydrogen atoms, this means the sample contains \(\frac{6}{12} = 0.5\) moles of the compound \(\left(\mathrm{NH}_{4}\right)_{3}\mathrm{PO}_{4}\).

Calculate the moles of oxygen in the sample

Determine the number of moles of oxygen atoms in the compound. There are 4 oxygen atoms in one molecule of \(\left(\mathrm{NH}_{4}\right)_{3}\mathrm{PO}_{4}\), so 0.5 moles of the compound will contain 0.5 * 4 = 2 moles of oxygen atoms.

Key concepts

Chemical Formula Calculation

Understanding the chemical formula calculation is essential when tackling stoichiometry problems. The chemical formula of a compound tells you the ratio of atoms of each element present in the compound. For instance, in the provided exercise, the chemical formula of ammonium phosphate is ewline ewline \(left(\mathrm{NH}_{4}\right)_{3}\mathrm{PO}_{4}\), which indicates that each molecule contains three ammonium ions \(\mathrm{NH}_{4}^{+}\), and one phosphate ion \(\mathrm{PO}_{4}^{3-}\). Analyzing the formula allows us to understand that each unit has 4 hydrogen atoms within the ammonium ions, and a total of 4 oxygen atoms associated with the phosphate ion. This knowledge is crucial for quantitatively describing chemical reactions and understanding the mole concept, as it serves as the groundwork for calculating the amount of each element in a given sample. The ability to calculate the number of atoms or moles of elements from the chemical formula is a foundational skill in chemistry.

Mole Concept

The mole concept is a bridge between the microscopic world of atoms and the macroscopic world we live in. A mole is defined as the amount of substance that contains as many entities (atoms, molecules, ions, etc.) as there are atoms in 12 grams of carbon-12. This number is known as Avogadro's number, which is approximately \(6.022 \times 10^{23}\).
For example, when the exercise states that there are 6 moles of hydrogen atoms in a sample of ammonium phosphate, it means that the sample contains \(6 \times 6.022 \times 10^{23}\) hydrogen atoms. Calculating the moles of different elements within a compound is a basic stoichiometry task, as it reveals the proportions in which substances react or are produced. In conjunction with the chemical formula, the mole concept allows you to determine the amount of each element in a compound and relate this to the mass of samples used in labs and industry.

Chemical Equations

Chemical equations are representations of chemical reactions in which the reactants are shown on the left side and the products on the right. They serve as a recipe for reactions, indicating not only what substances are involved but also their ratios. Balancing chemical equations is crucial because it ensures that the law of conservation of mass is followed, meaning that the same number of atoms of each element must be present on both sides of the equation.
This is where the mole concept becomes practical, as it allows us to convert the mass of substances into moles, which can then be used to balance the equation according to the stoichiometry of the reaction. In the context of the solve problems we're discussing, while we don't directly deal with a full reaction equation, the exercise relies on understanding the ratios of elements in the compound's chemical formula, which is, in a sense, a simplified equation indicating the formation of a compound from its constituent elements. Grasping these principles is essential for making predictions about the outcomes of chemical reactions and for practical applications in laboratory work.