Problem 61 - Chemistry The Central Science In Si Units

Question

Predict the chemical formulas of the ionic compound formed by (a) \(\mathrm{Fe}^{3+}\) and \(\mathrm{OH}^{-},\) (b) \(\mathrm{Cs}^{+}\) and \(\mathrm{NO}_{3}^{-}\), (c) \(\mathrm{V}^{2+}\) and \(\mathrm{CH}_{3} \mathrm{COO}^{-},(\mathbf{d}) \mathrm{Li}^{+}\) and \(\mathrm{PO}_{4}^{3-},(\mathbf{e}) \mathrm{In}^{3+}\) and \(\mathrm{O}^{2-} .\)

Step-by-Step Solution

Answer

The chemical formulas are (a) \(\mathrm{Fe(OH)}_{3}\), (b) \(\mathrm{CsNO_{3}}\), (c) \(\mathrm{V(CH_{3}COO)_{2}}\), (d) \(\mathrm{Li_{3}PO_{4}}\), (e) \(\mathrm{In_{2}O_{3}}\).

Step 1: Write Charges for Each Ion

Begin by writing the chemical symbol and charge for each ion involved in the pairing. These ion charges will help balance the overall charge of the compound.For part (a), ions are \(\mathrm{Fe}^{3+}\) and \(\mathrm{OH}^{-}\).For part (b), ions are \(\mathrm{Cs}^{+}\) and \(\mathrm{NO}_{3}^{-}\).For part (c), ions are \(\mathrm{V}^{2+}\) and \(\mathrm{CH}_{3}\mathrm{COO}^{-}\).For part (d), ions are \(\mathrm{Li}^{+}\) and \(\mathrm{PO}_{4}^{3-}\).For part (e), ions are \(\mathrm{In}^{3+}\) and \(\mathrm{O}^{2-}\).

Step 2: Determine the Formula for Each Pair

Create a neutral compound by balancing the total positive and negative charges for each pair of ions.(a) \(\mathrm{Fe}^{3+}\) and \(\mathrm{OH}^{-}\): Since 1 \(\mathrm{Fe}^{3+}\) requires 3 \(\mathrm{OH}^{-}\) ions to balance the charge, the formula is \(\mathrm{Fe(OH)}_{3}\).(b) \(\mathrm{Cs}^{+}\) and \(\mathrm{NO}_{3}^{-}\): Both ions have charges that cancel out directly, so the formula is \(\mathrm{CsNO}_{3}\).(c) \(\mathrm{V}^{2+}\) and \(\mathrm{CH}_{3}\mathrm{COO}^{-}\): 1 \(\mathrm{V}^{2+}\) matches with 2 \(\mathrm{CH}_{3}\mathrm{COO}^{-}\) ions, giving the formula \(\mathrm{V(CH}_{3}\mathrm{COO})_{2}\).(d) \(\mathrm{Li}^{+}\) and \(\mathrm{PO}_{4}^{3-}\): 3 \(\mathrm{Li}^{+}\) ions are needed per \(\mathrm{PO}_{4}^{3-}\) ion, resulting in the formula \(\mathrm{Li}_{3}\mathrm{PO}_{4}\).(e) \(\mathrm{In}^{3+}\) and \(\mathrm{O}^{2-}\): To balance the charges, 2 \(\mathrm{In}^{3+}\) ions are needed per 3 \(\mathrm{O}^{2-}\) ions, resulting in \(\mathrm{In}_{2}\mathrm{O}_{3}\).

Step 3: Review and Verify Charges

Check each formula to ensure charge neutrality and correct combination:- \(\mathrm{Fe}^{3+} + 3 \times \mathrm{OH}^{-} = 0\)- \(\mathrm{Cs}^{+} + \mathrm{NO}_{3}^{-} = 0\)- \(\mathrm{V}^{2+} + 2 \times \mathrm{CH}_{3}\mathrm{COO}^{-} = 0\)- \(3 \times \mathrm{Li}^{+} + \mathrm{PO}_{4}^{3-} = 0\)- \(2 \times \mathrm{In}^{3+} + 3 \times \mathrm{O}^{2-} = 0\)If all calculations hold true without errors, the formulas are correct!

Key Concepts

Balancing Chemical Equations

Balancing chemical equations is a foundational skill in chemistry that involves ensuring the same number of each type of atom appears on both sides of the equation. This balance reflects the law of conservation of mass, where mass is neither created nor destroyed in a chemical reaction. When balancing equations:

• Start by writing the unbalanced equation with the correct formulas for the reactants and products.
• Select an element that appears in one compound on each side of the equation.
• Adjust the coefficients of the compounds to balance the atoms for the chosen element.
• Continue to balance the other elements using coefficients.
• Double-check your work to ensure the number of atoms on both sides is the same.

Balancing is crucial not only for stoichiometric calculations but also for understanding the chemical behavior and quantities involved.

Ion Charges

Ion charges are critical in predicting how elements combine to form compounds. An ion is an atom or molecule with a net electric charge due to the loss or gain of one or more electrons. Cations are positively charged ions formed by losing electrons, whereas anions are negatively charged ions formed by gaining electrons.

• Metals, like \(\mathrm{Fe}^{3+}\), tend to form cations by losing electrons.
• Non-metals, such as \(\mathrm{OH}^{-}\), typically form anions by gaining electrons.

The charge of an ion can often be predicted by the element's position in the periodic table. For instance, alkali metals in Group 1 will generally have a \(+1\) charge, while halogens in Group 17 typically have a \(-1\) charge. Understanding these charges helps in forming stable ionic compounds.

Chemical Formula Prediction

Predicting chemical formulas involves combining ions to form compounds in such a way that the total charge is zero. This means the sum of positive and negative charges must cancel out. To predict formulas:

• Identify the charges of the ions involved.
• Determine the ratio of ions needed to balance the charges.
• For the compound \(\mathrm{Fe(OH)}_{3}\), one \(\mathrm{Fe}^{3+}\) ion pairs with three \(\mathrm{OH}^{-}\) ions, resulting in a neutral compound.
• Record the chemical formula, ensuring that the number of each type of ion matches the required ratio.

These predictions help simplify understanding and describing chemical reactions where these compounds might form or break down.

Charge Neutrality

Charge neutrality is the principle that states an ionic compound as a whole must be electrically neutral. This balance is achieved by correctly pairing the total number of positive and negative charges in the composition.

• For example, in \(\mathrm{Li}_{3}\mathrm{PO}_{4}\), three \(\mathrm{Li}^{+}\) ions are used to neutralize one \(\mathrm{PO}_{4}^{3-}\) ion.
• This results in a neutral compound, as the total positive charges from the lithium ions balance the negative charge from the phosphate ion.

If an equation or formula does not maintain charge neutrality, it indicates an error in the balancing or the prediction of chemical formulas.

Cation-Anion Pairing

Cation-anion pairing involves combining positively charged cations and negatively charged anions to form ionic compounds. The nature of ionic bonding is based on the strong electrostatic attraction between these oppositely charged ions.

• Stable ionic compounds, such as \(\mathrm{CsNO}_{3}\), arise when cations and anions are paired in specific ratios that neutralize their charges.
• The common technique for determining the correct pairing involves balancing the charges, thus predicting crystal structures or physical properties based on the composition.
• An understanding of cation-anion pairing is crucial for applications across various chemical industries, including pharmaceuticals and materials science.

This principle underscores the importance of charge balance while illustrating how different ions can interact to form stable substances.