Question

Small daily doses of lithium carbonate taken orally are often given to treat manic-depressive psychoses. This dosage maintains the level of lithium ion in the blood at about $1\times {10}^{-3}\mathrm{mol}/\mathrm{L}$ . a. What is the formula of lithium carbonate? b. What mass of lithium ion is present per liter of blood in these patients?

Short answer

a. The formula of lithium carbonate is $L{i}_{2}C{O}_3$. b. To find the mass of lithium ions per liter of blood, we have ${\displaystyle 1\times {10}^{-3}\mathrm{mol}{\mathrm{L}}^{-1}\times \frac{6.94\mathrm{g}}{1\mathrm{mol}}=6.94\times {10}^{-3}\mathrm{g}{\mathrm{L}}^{-1}}$. So, there is $6.94\times {10}^{-3}\mathrm{g}$ of lithium ion present per liter of blood in these patients.

Step-by-step solution

a. Find the formula of lithium carbonate

Lithium (Li) is an alkali metal with a +1 charge, and carbonate (CO₃) is a polyatomic ion with a -2 charge. To determine the formula of lithium carbonate, we need to balance the charges. Lithium (Li) has a +1 charge and carbonate (CO₃) has a -2 charge. We need to have two Li atoms (+1 each) to balance the -2 charge of the carbonate ion. So, the formula for lithium carbonate is Li₂CO₃.

Key concepts

Chemical Formula

A chemical formula represents the composition of a compound using symbols for the elements and numbers to show how many atoms of each element are present. Understanding how to write a chemical formula is essential in chemistry, as it provides insight into the structure and properties of a compound. In our example, lithium carbonate is composed of lithium (Li) and carbonate (CO₃).

To write the formula correctly, you start by identifying the individual components and their respective charges. For lithium carbonate, lithium is represented by Li and has a charge of +1. Carbonate is a polyatomic ion represented by CO₃ with a charge of -2. By applying the rules of charge balancing, which we'll explore in detail later on, you can deduce that two lithium ions are necessary to balance the charge of one carbonate ion. This results in the formula Li₂CO₃.

The chemical formula gives us a concise way to express the ratio of these ions in the compound, allowing scientists to predict and understand its behavior in various contexts. The practice of writing chemical formulas extends to numerous compounds and is a foundational skill in chemistry. This allows for a consistent method of representing chemical substances across the globe.

Ionic Compounds

Ionic compounds are made up of charged particles called ions. These ions are atoms or molecules that have gained or lost electrons, resulting in a charge. In an ionic compound, these ions are typically a mix of metals, which form positive ions (cations), and non-metals or polyatomic ions, which form negative ions (anions).

Lithium carbonate is an example of an ionic compound because it contains the metal lithium (Li), which forms a positive ion, and the polyatomic ion carbonate (CO₃), which forms a negative ion. These oppositely charged ions attract each other and form a neutral compound.

One of the key characteristics of ionic compounds is their ability to dissolve in water and other polar solvents, which can separate the ions and allow them to move freely. This is particularly relevant for lithium carbonate in medicinal contexts, as dissolving in the blood permits lithium ions to distribute uniformly, sustaining therapeutic effects. Understanding ionic bonds is crucial to predict their properties, such as melting points, solubility, and electrical conductivity, which vary based on the ions involved and their arrangement.

Charge Balancing

Charge balancing is an essential principle in constructing the chemical formulas of ionic compounds. It is based on the need to balance positive and negative charges to achieve electrical neutrality. This principle guides how many of each type of ion are needed to create a stable compound.

Consider lithium carbonate: lithium has a charge of +1, and carbonate has a charge of -2. To balance the charges, two lithium ions are required to neutralize the charge of one carbonate ion. By combining two +1 charges from lithium with one -2 charge from carbonate, the total charge becomes zero, leading to a neutral compound represented as Li₂CO₃.

This balance of charges is what allows the compound to be stable and exist naturally. Without charge balancing, the compound would not form correctly, and its chemical properties would be unpredictable. Mastery of charge balancing is crucial for students aiming to excel in chemistry, as it applies across all ionic compounds.