Problem 88 - Chemistry The Molecular Science

Question

A typical cement contains, by weight, \(65 \% \mathrm{CaO}, 20 \%\) \(\mathrm{SiO}_{2}, 5 \% \mathrm{Al}_{2} \mathrm{O}_{3}, 6 \% \mathrm{Fe}_{2} \mathrm{O}_{3},\) and \(4 \% \mathrm{MgO} .\) Determine the mass percent of each type of atom present. Then, determine an empirical formula of the material from the percent composition, setting the subscript of the least abundant element to 1.00 .

Step-by-Step Solution

Answer

The empirical formula is approximately \(\text{Ca}_{15}\text{Si}_4\text{Al}\text{Fe}\text{Mg}\).

Step 1: Determine the molar masses of each oxide

To solve this problem, we first need to determine the molar mass of each compound present in the cement:- \(\text{CaO} = 40.08 + 16.00 = 56.08 \, \text{g/mol}\)- \(\text{SiO}_2 = 28.09 + 2(16.00) = 60.09 \, \text{g/mol}\)- \(\text{Al}_2\text{O}_3 = 2(26.98) + 3(16.00) = 101.96 \, \text{g/mol}\)- \(\text{Fe}_2\text{O}_3 = 2(55.85) + 3(16.00) = 159.70 \, \text{g/mol}\)- \(\text{MgO} = 24.31 + 16.00 = 40.31 \, \text{g/mol}\)

Step 2: Calculate moles of each element in all compounds

Using the percent composition and molar mass, calculate the moles of each element in the oxides assuming 100 g of cement.- Ca in \(\text{CaO}: \frac{65}{56.08}\text{ g/mol}= 1.159\) mol of Ca- Si in \(\text{SiO}_2: \frac{20}{60.09}\text{ g/mol}= 0.333\) mol of Si- Al in \(\text{Al}_2\text{O}_3: \frac{5}{101.96}\text{ g/mol} \times 2 = 0.098\) mol of Al- Fe in \(\text{Fe}_2\text{O}_3: \frac{6}{159.70}\text{ g/mol} \times 2 = 0.075 \) mol of Fe- Mg in \(\text{MgO}: \frac{4}{40.31}\text{ g/mol} = 0.099 \) mol of Mg- O calculation is not needed at this step because we’re calculating individual elements without combining them into an empirical formula yet.

Step 3: Determine the empirical formula

To determine the empirical formula, divide the moles of each element by the smallest number of moles among the elements.- Ca: \(\frac{1.159}{0.075} = 15.45\)- Si: \(\frac{0.333}{0.075} = 4.44\)- Al: \(\frac{0.098}{0.075} = 1.31\)- Fe: \(\frac{0.075}{0.075} = 1.00\)- Mg: \(\frac{0.099}{0.075} = 1.32\)Rounding these to the nearest whole numbers: Chemical formula approximates to \(\text{Ca}_{15}\text{Si}_4\text{Al}_1\text{Fe}_1\text{Mg}_1\).

Key Concepts

Percent Composition

Understanding percent composition is crucial in analyzing chemical substances. It represents the percentage by weight of each element within a compound. In the context of cement, this becomes critical to determine how much of each substance, like calcium oxide or silicon dioxide, contributes to the overall composition.

To calculate the percent composition, you need to know the weight percentages of each component. For cement, if you have a 100-gram sample, each component's percentage can directly translate into grams. For instance, if cement is made up of 65% calcium oxide, this means there are 65 grams of calcium oxide in a 100-gram sample.

• The percent by weight lets us move seamlessly into calculating the moles of each element.
• Using these weight percentages, you can convert grams to moles, a step crucial for determining the empirical formula.
• This step helps in understanding the relative abundance of each element in the cement.

Grasping percent composition aids in connecting macroscopic samples to the microscopic understanding of its constituent atoms.

Molar Mass Calculation

Molar mass is a key concept in chemistry, underpinning calculations involving chemical formulas and reactions. It tells us the mass of one mole of a substance, allowing for conversions between mass and number of particles.

To find the molar mass of a compound, add together the atomic masses of all atoms in its formula. Let's illustrate this with calcium oxide (CaO):

• Calcium has an atomic mass of 40.08 g/mol and oxygen has 16.00 g/mol.
• Thus, the molar mass of calcium oxide is calculated as \(40.08 + 16.00 = 56.08 \) g/mol.

In the context of cement analysis:

• Knowing the molar masses of individual oxides allows us to calculate the number of moles of each element in a set amount of cement.
• These calculations are foundational for moving forward to find the empirical formula.

Molar mass serves as the bridge between the mass of a material sample and the number of atoms or molecules it contains.

Cement Chemical Analysis

Cement chemical analysis involves determining the composition and proportions of the components in cement. The goal is to identify the relative quantities of compounds and their individual elements.

Analysing these components helps us determine an empirical formula, which is a simplified, smallest ratio representation of the elements present. In this exercise, we calculated the moles of each element from the respective oxides' percent compositions and their molar masses.

• For example, identifying how much calcium, silicon, aluminum, iron, and magnesium come from calcium oxide, silicon dioxide, etc.
• This helps construct the cement's empirical formula – providing insight into which elements are more prevalent and how they might interact or contribute to the properties of the cement.
• Cement chemistry can vary, and analyzing the formula also assists in predicting durability and performance.

Ultimately, chemical analysis of cement not only tells us what is present but also how it relates to the material's usability and function in construction and beyond.