Question

Complete the table. \begin{tabular}{lcccc} Formula & Number of \(\mathrm{SO}_{4}{ }^{2-}\) Units & Number of Sulfur Atoms & Number of Oxygen Atoms & Number of Metal Atoms \\ \(\mathrm{CaSO}_{4}\) & \(-\) & \(-\) & \(-\) \\ \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) & \(-\) & \(-\) & \(-\) \\ \(\mathrm{K}_{2} \mathrm{SO}_{4}\) & \(-\) & \(-\) & \(-\) \\ \hline \end{tabular}

Short answer

\(\mathrm{CaSO}_{4}\): 1 \(\mathrm{SO}_{4}^{2-}\) unit, 1 sulfur, 4 oxygens, 1 calcium atom. \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\): 3 \(\mathrm{SO}_{4}^{2-}\) units, 3 sulfur, 12 oxygens, 2 aluminum atoms. \(\mathrm{K}_{2}\mathrm{SO}_{4}\): 1 \(\mathrm{SO}_{4}^{2-}\) unit, 1 sulfur, 4 oxygens, 2 potassium atoms.

Step-by-step solution

Analyze the Formula

The formula of a compound tells us the ratio of different elements present in the compound. Each \(\mathrm{SO}_{4}^{2-}\) unit consists of one sulfur (S) atom and four oxygen (O) atoms. Look at the subscript immediately following the element symbol to determine the number of atoms.

Fill in for Calcium Sulfate \(\mathrm{CaSO}_{4}\)

The formula \(\mathrm{CaSO}_{4}\) has no subscript after the sulfate part, indicating that there is one \(\mathrm{SO}_{4}^{2-}\) unit. Therefore, there is one sulfur atom and four oxygen atoms. Since there is one calcium atom (Ca), there are no subscripts after the symbol Ca.

Fill in for Aluminum Sulfate \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\)

In \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\), the subscript (3) outside the parentheses indicates that there are three \(\mathrm{SO}_{4}^{2-}\) units. Therefore, there are three sulfur atoms and \(4 \times 3 = 12\) oxygen atoms. The subscript (2) indicates there are two aluminum atoms (Al).

Fill in for Potassium Sulfate \(\mathrm{K}_{2}\mathrm{SO}_{4}\)

The formula \(\mathrm{K}_{2}\mathrm{SO}_{4}\) indicates that there is one \(\mathrm{SO}_{4}^{2-}\) unit. Hence, there is one sulfur atom and four oxygen atoms. The subscript (2) indicates that there are two potassium atoms (K).

Key concepts

Stoichiometry

Stoichiometry is a section of chemistry that deals with the quantitative relationships between the reactants and products in chemical reactions. It helps us to calculate how much of each substance is needed or produced in a reaction. Stoichiometry is based on the law of conservation of mass, which states that in any chemical reaction, matter is neither created nor destroyed.

When working on stoichiometric calculations, the first step is understanding the chemical formula of the compounds involved. Each formula provides a recipe for how atoms are combined to make a molecule or ionic compound. For instance, in a formula such as \( \mathrm{CaSO}_{4} \), stoichiometry tells us that one atom of calcium (Ca) reacts with one sulfate unit (\(\mathrm{SO}_{4}^{2-}\)) to produce calcium sulfate. By using stoichiometry, students can determine vital information like the number of metal, sulfur, and oxygen atoms present in a sample of the compound.

Chemical Notation

Chemical notation is a standardized method of representing elements and compounds in a concise and informative way. Elements are represented by their chemical symbols, such as Ca for calcium and S for sulfur, taken from the periodic table of elements. Subscripts are used to show the number of atoms of an element present: \( H_2O \) indicates there are two hydrogen atoms for each oxygen atom in water.

Chemical notation also includes the use of parentheses and coefficients. Parentheses group atoms together, showing that they are bound in a particular way, usually as a polyatomic ion. For instance, in \( \mathrm{Al}_{2}(\mathrm{SO}_{4})_{3} \) the \( \mathrm{SO}_{4} \) units are grouped together, indicating that each alumina molecule is combing with three sulfate units. This standardized system is vital because it allows chemists to convey complex information in a simple format.

Molecular Composition

The molecular composition describes the arrangement and number of atoms within a molecule, which is the smallest unit of a chemical compound that retains its chemical properties. Understanding a molecule's composition involves recognizing the types of atoms based on their symbols and counting how many of each are present.

This information not only tells us the ratio in which different atoms combine (for example, two hydrogen atoms to one oxygen atom for water), but also the spatial arrangement, which can affect the properties of the compound. In the compound \( \mathrm{K}_{2}\mathrm{SO}_{4} \), the molecular composition shows us that for every sulfate ion, there are two potassium ions, giving us insights into the physical characteristics and reactivity of the compound.