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Chapter 2: Problem 62

Predict the chemical formulas of the compounds formed by the following pairs of ions: (a) \(\mathrm{Cr}^{3+}\) and \(\mathrm{Br}^{-}\), (b) \(\mathrm{Fe}^{3+}\) and \(\mathrm{O}^{2-}\), (c) \(\mathrm{Hg}_{2}{ }^{2+}\) and \(\mathrm{CO}_{3}{ }^{2-}\), (d) \(\mathrm{Ca}^{2+}\) and \(\mathrm{ClO}_{3}^{-}\), (e) \(\mathrm{NH}_{4}^{+}\)and \(\mathrm{PO}_{4}{ }^{3-}\).

Short Answer

Expert verified
The chemical formulas of the compounds formed by the given pairs of ions are: (a) \(\mathrm{CrBr}_{3}\) (b) \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) (c) \(\mathrm{Hg}_{2}\mathrm{CO}_{3}\) (d) \(\mathrm{Ca}(\mathrm{ClO}_{3})_{2}\) (e) \(\mathrm{(NH}_{4}\mathrm{)_{3}PO}_{4}\)

Step by step solution

01

(a) \(\mathrm{Cr}^{3+}\) and \(\mathrm{Br}^{-}\)

To balance the charges, we need to find the least common multiple (LCM) of the two charges which in our case is 3. This means we need 3 \(\mathrm{Br}^-\) ions to balance the charge of one \(\mathrm{Cr}^{3+}\) ion. Therefore, the chemical formula of the compound formed by these ions is \(\mathrm{CrBr}_{3}\).
02

(b) \(\mathrm{Fe}^{3+}\) and \(\mathrm{O}^{2-}\)

To balance the charges, we need to find the least common multiple (LCM) of the two charges which in our case is 6. This means we need 2 \(\mathrm{O}^{2-}\) ions to balance the charge of 3 \(\mathrm{Fe}^{3+}\) ions. Therefore, the chemical formula of the compound formed by these ions is \(\mathrm{Fe}_{2}\mathrm{O}_{3}\).
03

(c) \(\mathrm{Hg}_{2}{ }^{2+}\) and \(\mathrm{CO}_{3}{ }^{2-}\)

In this case, the charges are already balanced as the positive charge is +2 and the negative charge is -2. Therefore, the chemical formula of the compound formed by these ions is \(\mathrm{Hg}_{2}\mathrm{CO}_{3}\).
04

(d) \(\mathrm{Ca}^{2+}\) and \(\mathrm{ClO}_{3}^{-}\)

To balance the charges, we need to find the least common multiple (LCM) of the two charges which in our case is 2. This means we need 2 \(\mathrm{ClO}_3^-\) ions to balance the charge of one \(\mathrm{Ca}^{2+}\) ion. Therefore, the chemical formula of the compound formed by these ions is \(\mathrm{Ca}(\mathrm{ClO}_{3})_{2}\).
05

(e) \(\mathrm{NH}_{4}^{+}\) and \(\mathrm{PO}_4^{3-}\)

To balance the charges, we need to find the least common multiple (LCM) of the two charges which in our case is 3. This means we need 3 \(\mathrm{NH}_4^+\) ions to balance the charge of one \(\mathrm{PO}_4^{3-}\) ion. Therefore, the chemical formula of the compound formed by these ions is \(\mathrm{(NH}_{4}\mathrm{)_{3}PO}_{4}\).

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Key Concepts

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

Understanding Ions
Ions are atoms or molecules that have gained or lost electrons, leading them to have a charge. This charge can be positive or negative:
  • Cations: Positively charged ions created when an atom loses electrons. For example, \( \mathrm{Cr}^{3+} \) is a cation because it has lost three electrons.
  • Anions: Negatively charged ions formed when an atom gains electrons. \( \mathrm{Br}^{-} \) is an anion, having gained one electron.
These ions combine to form compounds, balancing out their charges in the process.
Forming Compounds
Compounds are created when ions of opposite charges attract and bond. The key is to balance the charges so that the overall charge of the compound equals zero.
- **Example:** When \( \mathrm{Cr}^{3+} \) combines with \( \mathrm{Br}^{-} \), three \( \mathrm{Br}^{-} \) ions are needed to balance the charge of one \( \mathrm{Cr}^{3+} \), resulting in the formula \( \mathrm{CrBr}_{3} \).
This principle applies to all ionic compounds, ensuring that the total positive charges equal the total negative charges.
The Importance of Charge Balancing
Charge balancing is essential when predicting chemical formulas because it ensures stability in compounds. When unbalanced, compounds would have surplus charges, making them unstable.
- **How to Balance Charges:**
  • Determine the charge of each ion.
  • Find the least common multiple (LCM) of the charges.
  • Adjust the number of ions needed to balance the charges.
For example, with \( \mathrm{Fe}^{3+} \) and \( \mathrm{O}^{2-} \), the LCM is 6, meaning you require two \( \mathrm{O}^{2-} \) ions and three \( \mathrm{Fe}^{3+} \) ions to form \( \mathrm{Fe}_{2}\mathrm{O}_{3} \). This ensures the compound is neutral and stable.

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Most popular questions from this chapter

Give the chemical names of each of the following familiar compounds: (a) \(\mathrm{NaCl}\) (table salt), (b) \(\mathrm{NaHCO}_{3}\) (baking soda), (c) \(\mathrm{NaOCl}\) (in many bleaches), (d) \(\mathrm{NaOH}\) (caustic soda), (e) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}\) (smelling salts), (f) \(\mathrm{CaSO}_{4}\) (plaster of Paris).

Hydrogen sulfide is composed of two elements: hydrogen and sulfur. In an experiment, \(6.500 \mathrm{~g}\) of hydrogen sulfide is fully decomposed into its elements. (a) If \(0.384 \mathrm{~g}\) of hydrogen is obtained in this experiment, how many grams of sulfur must be obtained? (b) What fundamental law does this experiment demonstrate? (c) How is this law explained by Dalton's atomic theory?

Millikan determined the charge on the electron by studying the static charges on oil drops falling in an electric field (Figure 2.5). A student carried out this experiment using several oil drops for her measurements and calculated the charges on the drops. She obtained the following data: (a) What is the significance of the fact that the droplets carried different charges? (b) What conclusion can the student draw from these data regarding the charge of the electron? (c) What value (and to how many significant figures) should she report for the electronic charge?

Complete the table by filling in the formula for the ionic compound formed by each pair of cations and anions, as shown for the first pair.

Name the following ionic compounds: (a) \(\mathrm{KCN}\), (b) \(\mathrm{NaBrO}_{2}\), (c) \(\mathrm{Sr}(\mathrm{OH})_{2}\), (d) \(\mathrm{CoTe}\), (e) \(\mathrm{Fe}_{2}\left(\mathrm{CO}_{3}\right)_{3}\), (f) \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}\), (g) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{3}\), (h) \(\mathrm{NaH}_{2} \mathrm{PO}_{4}\), (i) \(\mathrm{KMnO}_{4}\), (j) \(\mathrm{Ag}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\).
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