Complete the table. \(\begin{array}{lccccc} & \begin{array}{c}\text { Number } \\ \text { of }\end{array} & \begin{array}{c}\text { Number } \\ \text { of }\end{array} & \begin{array}{c}\text { Number } \\ \text { of }\end{array} & \begin{array}{c}\text { Number } \\ \text { of }\end{array} & \begin{array}{c}\text { Number } \\ \text { of }\end{array} \\\ \begin{array}{l}\text { Formula } \\ \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-} \\ \text {Units }\end{array} & \begin{array}{c}\text { Carbon } \\ \text { Atoms } \\\ \begin{array}{l}\mathrm{Mg}\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)_{2}\end{array}\end{array} & \begin{array}{l}\text { Hydrogen } \\ \text { Atoms }\end{array} & \begin{array}{c}\text { Oxygen } \\\ \text { Atoms }\end{array} & \begin{array}{c}\text { Metal } \\ \text { Atoms }\end{array} \\ \mathrm{NaC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} & & & & \\\ \mathrm{Cr}_{2}\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)_{4} & & & & \end{array}\)

Step by step solution

01

Identify the compounds

We have the compounds: \( Mg(C_2H_3O_2)_2 \), \( NaC_2H_3O_2 \), and \( Cr_2(C_2H_3O_2)_4 \). The formula unit \( C_2H_3O_2^- \) is the acetate ion. In the compound \( Mg(C_2H_3O_2)_2 \) there are two acetate ions per magnesium ion. In \( NaC_2H_3O_2 \), there is one sodium ion per acetate ion. In \( Cr_2(C_2H_3O_2)_4 \), there are two chromium ions for every four acetate ions.

02

Count Atoms in Magnesium Acetate

In \( Mg(C_2H_3O_2)_2 \), there are two acetate ions. Each acetate ion has 2 carbon atoms, 3 hydrogen atoms, and 2 oxygen atoms. So, there are \( 2 \times 2 = 4 \) carbon atoms, \( 2 \times 3 = 6 \) hydrogen atoms, \( 2 \times 2 = 4 \) oxygen atoms, and 1 magnesium atom.

03

Count Atoms in Sodium Acetate

In \( NaC_2H_3O_2 \), there is one acetate ion per sodium ion. Therefore, there are 2 carbon atoms, 3 hydrogen atoms, and 2 oxygen atoms. and 1 sodium atom.

04

Count Atoms in Chromium Acetate

In \( Cr_2(C_2H_3O_2)_4 \), there are four acetate ions. As such, there are \( 4 \times 2 = 8 \) carbon atoms, \( 4 \times 3 = 12 \) hydrogen atoms, \( 4 \times 2 = 8 \) oxygen atoms, and 2 chromium atoms.

05

Fill in the table

The completed table is:\(\begin{array}{|l|c|c|c|c|}\hline & \text{Carbon atoms} & \text{Hydrogen atoms} & \text{Oxygen atoms} & \text{Metal atoms} \ \hline \text{Mg}(C_2H_3O_2)_2 & 4 & 6 & 4 & 1 \ \hline NaC_2H_3O_2 & 2 & 3 & 2 & 1 \ \hline Cr_2(C_2H_3O_2)_4 & 8 & 12 & 8 & 2 \ \hline \end{array}\)

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Formulas

Understanding chemical formulas is crucial in mastering stoichiometry, which is the study of the quantitative relationships between the substances involved in chemical reactions. Chemical formulas provide a shorthand representation of the composition of substances, indicating the types and numbers of atoms present in the smallest unit of the substance, which could be a molecule or a formula unit.

For example, the chemical formula for table salt is NaCl, indicating that each formula unit consists of one sodium (Na) atom and one chlorine (Cl) atom. In a compound such as magnesium acetate, represented by the formula \( Mg(C_2H_3O_2)_2 \), the parentheses and subscript outside them tell us that there are two acetate ions (\( C_2H_3O_2^- \)) for each magnesium ion (Mg). Thus, decoding chemical formulas is the first step in quantifying the elements that make up a compound and their ratios—a fundamental task in stoichiometry.

Mole Concept

The mole concept is a bridge between the microscopic world of atoms and the macroscopic world that we can observe and measure. One mole is defined as exactly 6.022 x 10^23 entities (Avogadro's number), whether they are atoms, molecules, ions, or other particles. This number is chosen because it corresponds to the number of atoms in exactly 12 grams of carbon-12, establishing a universal basis for the mole.

When working with reactions and compounds in chemistry, we often use the mole as a unit to express amounts of a chemical substance. For example, saying that a reaction requires one mole of sodium acetate (\( NaC_2H_3O_2 \)) means it requires 6.022 x 10^23 formula units of sodium acetate. The mole concept enables chemists to count atoms and molecules in a practical way, making it easier to predict how much of each reactant is needed and how much of each product will be made in a chemical reaction.

Atom Counting

Atom counting is the process of determining the number of each type of atom in a compound. This is often done using the compound's chemical formula, as seen in the exercise with magnesium acetate (\( Mg(C_2H_3O_2)_2 \)), sodium acetate (\( NaC_2H_3O_2 \)), and chromium acetate (\( Cr_2(C_2H_3O_2)_4 \)). The subscripts in the chemical formula indicate the number of each type of atom in the smallest unit of the compound. To count atoms in a compound with multiple identical groups, such as in chromium acetate, you multiply the number of groups (in this case, acetate ions) by the number of each atom within one group.

Atom counting becomes particularly valuable when you are balancing chemical equations and need to ensure that the same number of each type of atom is present on both sides of the equation. It's also essential for tasks such as determining the empirical or molecular formulas of compounds based on their percent composition by mass.