Question

Give the formulas of all the compounds containing no ions other than \(\mathrm{K}^{+}, \mathrm{Ca}^{2+}, \mathrm{Cl}^{-},\) and \(\mathrm{S}^{2-}\).

Short answer

Answer: The possible compounds are \(\mathrm{KCl}\), \(\mathrm{K_2S}\), \(\mathrm{CaCl_2}\), and \(\mathrm{CaS}\).

Step-by-step solution

Analyze the given ions and their charges.

The problem provides us with 4 ions: 1. \(\mathrm{K}^{+}\) has a charge of +1 2. \(\mathrm{Ca}^{2+}\) has a charge of +2 3. \(\mathrm{Cl}^{-}\) has a charge of -1 4. \(\mathrm{S}^{2-}\) has a charge of -2 Keep in mind that when combining ions to form compounds, the total charge should be zero. In other words, the number of positive charges should equal the number of negative charges.

Combine the ions in possible combinations to form neutral compounds

Let's consider all possible combinations of the ions. 1. \(\mathrm{K}^{+}\) and \(\mathrm{Cl}^{-}\) - Charges: +1 and -1 - As their charges are equal and opposite, they can combine in a 1:1 ratio to form a neutral compound. 2. \(\mathrm{K}^{+}\) and \(\mathrm{S}^{2-}\) - Charges: +1 and -2 - In order to balance the charges, we need two \(\mathrm{K}^{+}\) ions for each \(\mathrm{S}^{2-}\) ion. The ratio is 2:1. 3. \(\mathrm{Ca}^{2+}\) and \(\mathrm{Cl}^{-}\) - Charges: +2 and -1 - Similarly, we need two \(\mathrm{Cl}^{-}\) ions for each \(\mathrm{Ca}^{2+}\) ion to balance the charges. The ratio is 1:2. 4. \(\mathrm{Ca}^{2+}\) and \(\mathrm{S}^{2-}\) - Charges: +2 and -2 - As their charges are equal and opposite, they can combine in a 1:1 ratio to form a neutral compound.

Write down the formulas of the compounds

Based on the previous step, we have the following compounds: 1. \(\mathrm{K}^{+}\) and \(\mathrm{Cl}^{-}\): In a 1:1 ratio, their formula is: \(\mathrm{KCl}\). 2. \(\mathrm{K}^{+}\) and \(\mathrm{S}^{2-}\): When combined in a 2:1 ratio, their formula is: \(\mathrm{K_2S}\). 3. \(\mathrm{Ca}^{2+}\) and \(\mathrm{Cl}^{-}\): Combining in a 1:2 ratio, their formula is: \(\mathrm{CaCl_2}\). 4. \(\mathrm{Ca}^{2+}\) and \(\mathrm{S}^{2-}\): With a 1:1 ratio, their formula is: \(\mathrm{CaS}\). In conclusion, the compounds formed from the given ions are: \(\mathrm{KCl}\), \(\mathrm{K_2S}\), \(\mathrm{CaCl_2}\), and \(\mathrm{CaS}\).

Key concepts

Chemical Nomenclature

Understanding chemical nomenclature is akin to learning the alphabet of chemistry. It's the standard method for naming chemical substances such as elements, compounds, and ions, providing a unique identifier for each. For instance, potassium ion is denoted as \(\mathrm{K}^+\) and chloride ion as \(\mathrm{Cl}^-\). When these two ions combine to form a compound, the resulting substance is called potassium chloride, with a formula of \(\mathrm{KCl}\).

Similarly, we denote calcium as \(\mathrm{Ca}^{2+}\) and sulfide ion as \(\mathrm{S}^{2-}\). When combined, they form calcium sulfide, with the formula \(\mathrm{CaS}\). The nomenclature tells us not only the elements present but also their proportions. For a beginner, remembering these symbols and their corresponding names can be challenging, but it is essential for communicating effectively in the study of chemistry.

Charge Balance in Ionic Compounds

Ionic compounds are formed when positively charged ions (cations) and negatively charged ions (anions) are bound together by electrostatic forces. The fundamental rule for constructing these compounds is that the total charge must balance out to zero. This is why a potassium ion \(\mathrm{K}^+\) can pair with a chloride ion \(\mathrm{Cl}^-\) in a 1:1 ratio to form potassium chloride (\mathrm{KCl}), as their charges (+1 and -1, respectively) neutralize each other.

However, when ions have different charges, such as a \(\mathrm{K}^+\) ion and sulfide ion \(\mathrm{S}^{2-}\), we must use more than one potassium ion to balance the double negative charge of sulfide. That's why the formula for potassium sulfide is \(\mathrm{K_2S}\), indicating that two potassium ions are needed to balance the charge of one sulfide ion. Correct charge balance is crucial for the stability of an ionic compound and is a fundamental aspect of chemistry that guides the formulation of chemical compounds.

Stoichiometry

Stoichiometry is the mathematics behind chemistry. It deals with the quantitative relationship between reactants and products in a chemical reaction. In the context of forming ionic compounds, stoichiometry ensures that the number of atoms of each element is balanced, reflecting the law of conservation of mass.

For example, when we combine calcium ions \(\mathrm{Ca}^{2+}\) with chloride ions \(\mathrm{Cl}^-\) to form calcium chloride (\mathrm{CaCl_2}), we use stoichiometry to determine that we need two chloride ions for every one calcium ion. This is because the calcium ion has a +2 charge, while each chloride ion has a -1 charge. Stoichiometry helps ensure that all charges are balanced and that the substance is electrically neutral. Learning stoichiometry allows students to predict the amounts of substances consumed and produced in any chemical reaction, giving them a powerful tool for practical applications in chemistry.