Question

Lithium oxide \(\left(\mathrm{Li}_{2} \mathrm{O}\right.\), molecular weight \(=30 \mathrm{~g} / \mathrm{mole}\) ) reacts with water \(\left(\mathrm{H}_{2} \mathrm{O}\right.\), molecular weight \(=18 \mathrm{~g} /\) mole, density \(=1.0\) \(\mathrm{g} / \mathrm{cm}^{3}\) ) to produce lithium hydroxide ( \(\mathrm{LiOH}\) ) according to the following reaction: \(\mathrm{Li}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}+2 \mathrm{LiOH}\). What mass of \(\mathrm{Li}_{2} \mathrm{O}\) is required to completely react with 24 liters of \(\mathrm{H}_{2} \mathrm{O} ?\)

Short answer

40,000 grams of lithium oxide (Li₂O) is required to completely react with 24 liters of water (H₂O).

Step-by-step solution

Convert volume of water to mass

The density of water is given as 1.0 g/cm³, and we are given 24 liters of water. We first need to convert liters to cubic centimeters (cm³), and then multiply by the density to get the mass of water: \(24 \,\text{liters} × 1000\frac{\text{cm}^{3}}{1 \,\text{liters}} = 24000\text{cm}^3\) Then: \(24000\,\text{cm}^3 × 1.0\frac{g}{\text{cm}^3} = 24000\,g\)

Determine the number of moles of water

Now, we will use the molecular weight of water to convert the mass of water to moles: \(\text{Number of moles} =\frac{\text{Mass of H}_2\text{O}}{\text{Molecular weight of H}_2\text{O}} \) \(\text{Number of moles} =\frac{24000\,g}{18\,g/\text{mole}} = 1333.33\, \text{moles}\)

Use stoichiometry to find the number of moles of lithium oxide needed

According to the balanced chemical equation, 1 mole of Li₂O reacts with 1 mole of H₂O to produce 2 moles of LiOH. So, the moles of Li₂O needed will be equal to the moles of H₂O: \(\text{Number of moles of Li}_2\text{O} = 1333.33\, \text{moles}\)

Convert moles of lithium oxide to mass

Finally, we will use the molecular weight of Li₂O to convert the moles of Li₂O to mass: \(\text{Mass of Li}_2\text{O} = \text{Number of moles of Li}_2\text{O} × \text{Molecular weight of Li}_2\text{O} \) \(\text{Mass of Li}_2\text{O} = 1333.33\text{moles} × 30\frac{g}{\text{mole}} = 40,000\,g\) So, 40,000 grams of lithium oxide (Li₂O) is required to completely react with 24 liters of water (H₂O).

Key concepts

Lithium Oxide

Lithium oxide is a chemical compound with the formula \( \mathrm{Li}_2 \mathrm{O}\\), known for being an important compound in lithium chemistry. It is made up of two lithium (Li) atoms and one oxygen (O) atom. This compound is white and solid at room temperature, and it is one of the primary sources of lithium ions for chemical reactions.
When lithium oxide reacts with water, it leads to the formation of lithium hydroxide (LiOH). This process is a basic example of a chemical reaction, specifically a type of reaction known as a combination. In this reaction, lithium oxide combines with water to form a single product, lithium hydroxide.
Lithium is a fantastic element due to its unique properties. It is the lightest metal in the periodic table. Using lithium oxide, scientists can produce significant compounds used in batteries, glassworks, and even as protective layers for nuclear reactors.

Water Density

Water is a universally important solvent in chemical reactions. Understanding its density is crucial when converting between volume and mass. The density of a substance is defined as its mass per unit of volume and is expressed in units like grams per cubic centimeter (g/cm³).
Water is often used as the standard for measuring density. Its density is conventionally set to 1.0 g/cm³ at 4°C, which means 1 cubic centimeter of water weighs 1 gram. This property simplifies calculations and is a helpful reference point for many scientific experiments and reactions.
In chemical reactions involving liquids such as water, knowing the density allows for converting between volume and mass, which is essential for stoichiometric calculations. For example, when given a specific volume of water, multiplying by its density will provide the mass required for further calculations.

Molar Mass

The concept of molar mass is central to chemical stoichiometry. It refers to the mass of one mole of a substance, measured in grams per mole (g/mol). This value is critical for converting between the number of moles of a substance and its mass.
For a compound like lithium oxide \( \mathrm{Li}_2 \mathrm{O}\\), the molar mass is calculated by adding the atomic masses of all atoms within the compound:

• Lithium (Li) has an atomic mass of about 6.94 g/mol.
• Oxygen (O) has an atomic mass of about 16.00 g/mol.

Thus, the molar mass of lithium oxide is \(2 \times 6.94 + 16.00 = 29.88\approx 30\ g/mol\). Understanding this allows chemists to predict how much of a compound is needed when given the number of moles, facilitating precise chemical reactions.

Chemical Reactions

Chemical reactions are processes where substances (reactants) transform into new substances (products). In the context of lithium oxide and water reaction, the chemical equation is written as:\( \mathrm{Li}_2 \mathrm{O} + \mathrm{H}_2 \mathrm{O} \rightarrow 2 \mathrm{LiOH}\\).
This equation shows a one-to-one ratio of reactants leading to the formation of a specified amount of product. Chemical equations must always be balanced because of the law of conservation of mass, which states that matter cannot be created or destroyed in a closed system.
In our example, there is a perfect stoichiometric balance between the amounts of lithium oxide and water needed. This balance helps in predicting the amounts of products formed from specific amounts of reactants. Stoichiometry allows scientists to calculate precisely how much of each substance should be used to yield a particular product, vital for effective lab work and industrial processes.