Problem 25 - General Chemistry: Principles and Modern Applications

Question

Determine the percent, by mass, of the indicated element: (a) \(\mathrm{Pb}\) in tetraethyl lead, \(\mathrm{Pb}\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{4},\) once extensively used as an additive to gasoline to prevent engine knocking (b) Fe in Prussian blue, \(\mathrm{Fe}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]_{3},\) a pigment used in paints and printing inks (c) \(\mathrm{Mg}\) in chlorophyll, \(\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{MgN}_{4} \mathrm{O}_{5},\) the green pigment in plant cells

Step-by-Step Solution

Answer

As these problems are computational in nature, we will need to calculate the values individually. It involves using the atomic weights from the periodic table, and completing several percent composition calculations.

Step 1: Determine the Molar Mass of the Compounds

Use the atomic masses from the periodic table to determine the molar mass of each compound: (a) Tetraethyl lead, \(\mathrm{Pb}\left(\mathrm{C}_{2}\mathrm{H}_{5}\right)_{4}\)(b) Prussian blue, \(\mathrm{Fe}_{4}[\mathrm{Fe}(\mathrm{CN})_{6}]_{3}\)(c) Chlorophyll, \(\mathrm{C}_{55}\mathrm{H}_{72}\mathrm{MgN}_{4}\mathrm{O}_{5}\)

Step 2: Calculate the Molar Mass of the Indicated Element

Next, calculate the molar mass of the indicated element multyplying the atomic mass of the element by the amount of atoms of the given element instances in the formula:(a) Lead: \(Pb\)(b) Iron: \(Fe\)(c) Magnesium: \(Mg\)

Step 3: Find the Percent Composition

Finally, find the percent composition of the desired element in the compound using the formula:Percent Composition = \((mass \ of \ element/mass \ of \ compound) × 100%\)Substitute the values in for each compound and element and solve for the percent composition.

Key Concepts

Molar Mass Calculation

Molar mass is the mass of a given substance divided by the amount of substance in moles. It's essential in chemistry for converting between the mass of a compound and the amount of substance. To find the molar mass of a compound, you sum up the atomic masses of all the atoms in its formula.
For example, in tetraethyl lead, \( \mathrm{Pb}\left(\mathrm{C}_{2}\mathrm{H}_{5}\right)_{4} \), you calculate the molar mass by adding:

• The atomic mass of lead (\( \mathrm{Pb} \))
• Four times the atomic mass of carbon (\( \mathrm{C} \))
• Twenty times the atomic mass of hydrogen (\( \mathrm{H} \))

Understanding molar mass helps in determining how much of an element is in a compound, crucial for calculations like percent composition.

Atomic Mass

The atomic mass of an element is the average mass of its atoms, usually expressed in atomic mass units (amu). It's found on the periodic table.
When calculating the percent composition of an element in a compound, atomic mass is multiplied by the number of atoms of that element in the formula. For instance:

• For lead (\( \mathrm{Pb} \)) in tetraethyl lead, use the atomic mass of \( \mathrm{Pb} \)
• For iron (\( \mathrm{Fe} \)) in Prussian blue, use the atomic mass of \( \mathrm{Fe} \)
• For magnesium (\( \mathrm{Mg} \)) in chlorophyll, use the atomic mass of \( \mathrm{Mg} \)

Accurate atomic masses are crucial for achieving correct percent composition results, affecting how we understand the makeup of chemical compounds.

Chemical Compounds

Chemical compounds are substances made up of two or more different elements bonded together in specific ratios. Each compound has a chemical formula that exactly indicates the number and type of atoms.
Consider three compounds:

• Tetraethyl lead: \( \mathrm{Pb}\left(\mathrm{C}_{2}\mathrm{H}_{5}\right)_{4} \)
• Prussian blue: \( \mathrm{Fe}_{4}[\mathrm{Fe}(\mathrm{CN})_{6}]_{3} \)
• Chlorophyll: \( \mathrm{C}_{55}\mathrm{H}_{72}\mathrm{MgN}_{4}\mathrm{O}_{5} \)

The structure and formula of a compound dictate its chemical properties and behavior. Identifying the compound's formula is the first step in calculating molar mass and understanding its elemental composition.

Elemental Analysis

Elemental analysis involves determining the percentage composition of each element in a compound. It helps chemists understand the compound's detailed makeup and guides its usage in various applications.
To perform elemental analysis, follow these steps:

• Determine the total molar mass of the compound.
• Calculate the molar mass of the specific element within the compound.
• Use the formula for percent composition: \[\text{Percent Composition} = \left(\frac{\text{mass of element}}{\text{mass of compound}}\right) \times 100\%\]

Elemental analysis not only shows the proportion of elements present but also assists in recognizing the compound's potential use in various industries.