Question

The active ingredient of some antiperspirants is \(\mathrm{Al}_{2}(\mathrm{OH})_{5} \mathrm{Cl} .\) Calculate the mass percent of each element in this ingredient.

Short answer

Question: Find the mass percent of each element in the compound Al₂(OH)₅Cl. Answer: To find the mass percent of each element in the compound Al₂(OH)₅Cl, perform the following steps: 1. Calculate the molar mass of Al₂(OH)₅Cl: (2 × 26.98 g/mol) + (5 × ((1 × 16.00 g/mol) + (1 × 1.01 g/mol))) + (1 × 35.45 g/mol) 2. Determine the mass of each element in the compound: - Mass of Al: 2 × 26.98 g/mol - Mass of O: 5 × 16.00 g/mol - Mass of H: 5 × 1.01 g/mol - Mass of Cl: 1 × 35.45 g/mol 3. Calculate the mass percent of each element using their respective masses and the molar mass of Al₂(OH)₅Cl: - Mass percent of Al: (2 × 26.98 g/mol) / molar mass of Al₂(OH)₅Cl × 100% - Mass percent of O: (5 × 16.00 g/mol) / molar mass of Al₂(OH)₅Cl × 100% - Mass percent of H: (5 × 1.01 g/mol) / molar mass of Al₂(OH)₅Cl × 100% - Mass percent of Cl: (1 × 35.45 g/mol) / molar mass of Al₂(OH)₅Cl × 100% After performing these steps and calculations, you will obtain the mass percent of each element in Al₂(OH)₅Cl.

Step-by-step solution

Find the molar mass of Al₂(OH)₅Cl

To find the molar mass of the compound, we need to add the molar masses of all the elements present in the compound multiplied by their respective number of atoms. The molar masses of the elements are: - Al: 26.98 g/mol - O: 16.00 g/mol - H: 1.01 g/mol - Cl: 35.45 g/mol So, the molar mass of Al₂(OH)₅Cl is: (2 × 26.98 g/mol) + (5 × ((1 × 16.00 g/mol) + (1 × 1.01 g/mol))) + (1 × 35.45 g/mol)

Calculate the mass of each element in the compound

Now that we have the molar mass of Al₂(OH)₅Cl, we will find the mass of each element in the compound. - Mass of Al: 2 × 26.98 g/mol - Mass of O: 5 × 16.00 g/mol - Mass of H: 5 × 1.01 g/mol - Mass of Cl: 1 × 35.45 g/mol

Calculate the mass percent of each element

To find the mass percent of each element, we will divide the mass of each element by the molar mass of Al₂(OH)₅Cl and then multiply by 100. - Mass percent of Al: (2 × 26.98 g/mol) / molar mass of Al₂(OH)₅Cl × 100% - Mass percent of O: (5 × 16.00 g/mol) / molar mass of Al₂(OH)₅Cl × 100% - Mass percent of H: (5 × 1.01 g/mol) / molar mass of Al₂(OH)₅Cl × 100% - Mass percent of Cl: (1 × 35.45 g/mol) / molar mass of Al₂(OH)₅Cl × 100% Perform the calculations for each of the mass percent values above using the calculated molar mass of Al₂(OH)₅Cl from Step 1, and you will have the mass percent of each element in the compound.

Key concepts

Molar Mass

To calculate the mass percent of each element in a compound like \(\mathrm{Al}_2(\mathrm{OH})_5 \mathrm{Cl}\), we first need to determine its molar mass.
The molar mass of a compound is the sum of the molar masses of its constituent elements multiplied by their respective numbers of atoms. This serves as the base to convert moles into grams and vice-versa.
In this exercise, to find the molar mass of \(\mathrm{Al}_2(\mathrm{OH})_5 \mathrm{Cl}\), use the molar mass values:

• Aluminum (Al): 26.98 g/mol
• Oxygen (O): 16.00 g/mol
• Hydrogen (H): 1.01 g/mol
• Chlorine (Cl): 35.45 g/mol

Calculate for each part:
- Aluminum: \(2 \times 26.98\) g/mol
- Oxygen in hydroxyl: \(5 \times 16.00\) g/mol
- Hydrogen in hydroxyl: \(5 \times 1.01\) g/mol
- Chlorine: \(1 \times 35.45\) g/mol
This gives you the total molar mass of the compound by summing all these products, providing the grounded values needed to perform mass-related calculations.

Elemental Composition

Understanding the elemental composition of a compound like \(\mathrm{Al}_2(\mathrm{OH})_5 \mathrm{Cl}\) is crucial for determining the mass percent of each element in the compound.
Elemental composition helps us know the number and kinds of atoms present. For our compound:

• Each molecule has 2 aluminum atoms
• 5 hydroxide groups (each with 1 oxygen and 1 hydrogen atom)
• 1 chlorine atom

From these atoms, derive the mass of each type:
- Two Al contribute: \(2 \times 26.98\) g
- Five O contribute: \(5 \times 16.00\) g
- Five H contribute: \(5 \times 1.01\) g
- One Cl contributes: \(1 \times 35.45\) g
This means that if we know the total weight of each molecule, we can figure out what fraction is made up by each type of atom.
These weights help to establish how much each element contributes to the overall weight of the compound, setting the stage for calculating the mass percent.

Antiperspirant Chemistry

Antiperspirants are fascinating in their chemistry, and compounds like \(\mathrm{Al}_2(\mathrm{OH})_5 \mathrm{Cl}\) are key players.
Aluminum-based compounds are often active ingredients because they play an essential role in reducing underarm sweat.
This happens by temporarily blocking the sweat pores.
Specifically, the aluminum ions react with electrolytes in the sweat to form a gel-like plug.

• This gel plug constricts the opening of sweat ducts, preventing sweat from reaching the skin's surface.
• It acts as a barrier, giving a dry feel.

Breaking down the composition of such compounds helps manufacturers and users alike to understand how these products work at the elemental level, encouraging innovations.
Recognizing the elemental contribution shows that each component, from the aluminum to the hydroxide, plays a part in the efficacy and safety of the antiperspirant.