Problem 131 - Chemistry The Central Science

Question

One method to synthesize ionic solids is by the heating of two reactants at high temperatures. Consider the reaction of FeO with \(\mathrm{TiO}_{2}\) to form FeTiO \(_{3} .\) Determine the amount of each of the two reactants to prepare 2.500 \(\mathrm{g}\) FeTiO \(_{3},\) assuming the reaction goes to completion. (a) Write a balanced chemical reaction. (b) Calculate the formula weight of FeTiO_{3} . (c) Determine the moles of FeTiO_{3} . (d) Determine moles and mass (g) of FeO required. (e) Determine moles and mass (g) of TiO_ \(_{2}\) required.

Step-by-Step Solution

Answer

To synthesize 2.500 g of FeTiO₃, 1.184 g of FeO and 1.316 g of TiO₂ are required.

Step 1: (a) Write a balanced chemical reaction.

The balanced chemical reaction between FeO and TiO₂ to form FeTiO₃ can be written as: FeO + TiO₂ -> FeTiO₃

Step 2: (b) Calculate the formula weight of FeTiO₃.

The formula weight of FeTiO₃ can be found using the molar masses of Fe, Ti, and O atoms: FeTiO₃ = (55.84 g/mol * 1) + (47.87 g/mol * 1) + (16.00 g/mol * 3) FeTiO₃ = 55.84 + 47.87 + 48.00 = 151.71 g/mol

Step 3: (c) Determine the moles of FeTiO₃.

To find the moles of FeTiO₃, we can use the given mass and the formula weight: moles of FeTiO₃ = mass / formula weight moles of FeTiO₃ = 2.500 g / 151.71 g/mol = 0.01647 mol

Step 4: (d) Determine moles and mass (g) of FeO required.

From the balanced chemical equation, we know that 1 mol of FeO is needed to produce 1 mol of FeTiO₃. Therefore, the moles of FeO required can be calculated as: moles of FeO = moles of FeTiO₃ = 0.01647 mol Next, we can find the mass of FeO using its molar mass (71.84 g/mol): mass of FeO = moles * molar mass mass of FeO = 0.01647 mol * 71.84 g/mol = 1.184 g

Step 5: (e) Determine moles and mass (g) of TiO₂ required.

Similar to (d), from the balanced chemical equation, we know that 1 mol of TiO₂ is needed to produce 1 mol of FeTiO₃. Therefore, the moles of TiO₂ required can be calculated as: moles of TiO₂ = moles of FeTiO₃ = 0.01647 mol Next, we can find the mass of TiO₂ using its molar mass (79.87 g/mol): mass of TiO₂ = moles * molar mass mass of TiO₂ = 0.01647 mol * 79.87 g/mol = 1.316 g To synthesize 2.500 g of FeTiO₃, 1.184 g of FeO and 1.316 g of TiO₂ are required.

Key Concepts

Chemical Reaction Balancing

Understanding chemical reaction balancing is crucial when engaging in the synthesis of ionic solids like FeTiO₃. Balancing a chemical equation ensures that the law of conservation of mass is respected; the number of atoms of each element must be the same on both sides of the equation.

This balancing act isn't just a formal requirement; it's central to predicting how much of each reactant is needed to create a product. In our example, the balanced equation is FeO + TiO₂ -> FeTiO₃. Notice that the equation indicates a straightforward 1:1 ratio: one mole of FeO reacts with one mole of TiO₂ to produce one mole of FeTiO₃.

Formula Weight Calculation

The formula weight calculation is a pivotal step in stoichiometry, especially when determining how much of each substance is involved in a chemical reaction. Formula weight is the sum of the atomic weights of all the atoms in a chemical formula, and for ionic compounds like FeTiO₃, this gives us insight into how heavy a single mole of the substance is.

To calculate the formula weight of FeTiO₃, you add the atomic weights of one iron (Fe) atom, one titanium (Ti) atom, and three oxygen (O) atoms. The calculation gives us a formula weight of 151.71 g/mol. Knowing this allows us to determine how much of each reactant we’ll need to create a specific mass of the product.

Mole Concept

The mole concept is a fundamental cornerstone of chemistry that helps quantify substances within a chemical reaction. One mole represents Avogadro's number (\(6.022 \times 10^{23}\) atoms, molecules, or ions) and is a bridge between the micro world of atoms and the macro world we can measure.

In the context of synthesizing ionic solids, converting the given mass of FeTiO₃ (2.500 g) to moles allows us to use the balanced chemical equation to find the precise amount of reactants needed. This conversion is done by dividing the mass of FeTiO₃ by its formula weight, yielding approximately 0.01647 moles.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It incorporates all the previously mentioned concepts — chemical reaction balancing, formula weight, and the mole concept — to solve for quantities in a reaction.

Using stoichiometry, we conclude that to create 0.01647 moles (or 2.500 g) of FeTiO₃, we would require the same number of moles of FeO and TiO₂ since they react in a 1:1:1 ratio with FeTiO₃. Calculating the masses of these reactants involves multiplying their moles by their respective molar masses. This ensures that no reactant is wasted and the desired amount of product is obtained, an important consideration in any synthetic process.