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Chapter 12: Problem 131

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.

Short Answer

Expert verified
To synthesize 2.500 g of 贵别罢颈翱鈧�, 1.184 g of FeO and 1.316 g of TiO鈧� are required.

Step by step solution

01

(a) Write a balanced chemical reaction.

The balanced chemical reaction between FeO and TiO鈧� to form 贵别罢颈翱鈧� can be written as: FeO + TiO鈧� -> 贵别罢颈翱鈧�
02

(b) Calculate the formula weight of 贵别罢颈翱鈧�.

The formula weight of 贵别罢颈翱鈧� can be found using the molar masses of Fe, Ti, and O atoms: 贵别罢颈翱鈧� = (55.84 g/mol * 1) + (47.87 g/mol * 1) + (16.00 g/mol * 3) 贵别罢颈翱鈧� = 55.84 + 47.87 + 48.00 = 151.71 g/mol
03

(c) Determine the moles of 贵别罢颈翱鈧�.

To find the moles of 贵别罢颈翱鈧�, we can use the given mass and the formula weight: moles of 贵别罢颈翱鈧� = mass / formula weight moles of 贵别罢颈翱鈧� = 2.500 g / 151.71 g/mol = 0.01647 mol
04

(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 贵别罢颈翱鈧�. Therefore, the moles of FeO required can be calculated as: moles of FeO = moles of 贵别罢颈翱鈧� = 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
05

(e) Determine moles and mass (g) of TiO鈧� required.

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

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Reaction Balancing
Understanding chemical reaction balancing is crucial when engaging in the synthesis of ionic solids like 贵别罢颈翱鈧�. 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 + TiO鈧� -> 贵别罢颈翱鈧�. Notice that the equation indicates a straightforward 1:1 ratio: one mole of FeO reacts with one mole of TiO鈧� to produce one mole of 贵别罢颈翱鈧�.
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 贵别罢颈翱鈧�, this gives us insight into how heavy a single mole of the substance is.

To calculate the formula weight of 贵别罢颈翱鈧�, 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鈥檒l 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 贵别罢颈翱鈧� (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 贵别罢颈翱鈧� 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 鈥� chemical reaction balancing, formula weight, and the mole concept 鈥� to solve for quantities in a reaction.

Using stoichiometry, we conclude that to create 0.01647 moles (or 2.500 g) of 贵别罢颈翱鈧�, we would require the same number of moles of FeO and TiO鈧� since they react in a 1:1:1 ratio with 贵别罢颈翱鈧�. 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.

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Most popular questions from this chapter

Indicate whether this statement is true or false: If you want a semiconductor that emits blue light, you could either use a material that has a band gap corresponding to the energy of a blue photon or you could use a material that has a smaller band gap but make an appropriately sized nanoparticle of the same material.

Covalent bonding occurs in both molecular and covalent network solids. Which of the following statements best explains why these two kinds of solids differ so greatly in their hardness and melting points? $$ \begin{array}{l}{\text { (a) The molecules in molecular solids have stronger covalent bonding than covalent-network solids do. }} \\ {\text { (b) The molecules in molecular solids are held together by weak intermolecular interactions. }}\end{array} $$ $$ \begin{array}{l}{\text { (c) The atoms in covalent-network solids are more polarizable than those in molecular solids. }} \\ {\text { (d) Molecular solids are denser than covalent-network solids. }}\end{array} $$

Which type (or types) of crystalline solid is characterized by each of the following? (a) High mobility of electrons throughout the solid; (b) softness, relatively low melting point; (c) high melting point and poor electrical conductivity; ( \(\mathbf{d} )\) network of covalent bonds.

Both covalent-network solids and ionic solids can have melting points well in excess of room temperature, and both can be poor conductors of electricity in their pure form. However, in other ways their properties are quite different. $$ \begin{array}{l}{\text { (a) Which type of solid is more likely to dissolve in water? }} \\ {\text { (b) Which type of solid can become a considerably better }} \\ {\text { conductor of electricity via chemical substitution? }}\end{array} $$

Amorphous silica, \(\mathrm{SiO}_{2},\) has a density of about 2.2 \(\mathrm{g} / \mathrm{cm}^{3}\) , whereas the density of crystalline quartz, another form of \(\mathrm{SiO}_{2},\) is 2.65 \(\mathrm{g} / \mathrm{cm}^{3} .\) Which of the following statements is the best explanation for the difference in density? $$ \begin{array}{l}{\text { (a) Amorphous silica is a network-covalent solid, but quartz }} \\ {\text { is metallic. }} \\ {\text { (b) Amorphous silica crystallizes in a primitive cubic lattice. }} \\ {\text { (c) Quartz is harder than amorphous silica. }}\end{array} $$ $$ \begin{array}{l}{\text { (d) Quartz must have a larger unit cell than amorphous }} \\ {\text { silica. }}\end{array} $$ $$ \begin{array}{l}{\text { (e) The atoms in amorphous silica do not pack as efficiently }} \\ {\text { in three dimensions as compared to the atoms in quartz. }}\end{array} $$
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