Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Solve the following problem:

[tex]\[
\begin{array}{l}
=18(g) \\
=3(1) \cdot 87) \\
=56.46
\end{array}
\][/tex]

Example:
What is the percentage by mass in [tex]\(Al_2(SO_4)_3\)[/tex]?

(a) 149\%
(b) 25.39\%
(c) 50.39\%
(d) 59.25\%

Given:
[tex]\[ Al = 27, S = 32, O = 16 \][/tex]

Solution:
Aluminum sulfate: [tex]\[ Al_2(SO_4)_3 \][/tex]

Molar mass of aluminum sulfate:
[tex]\[ (27 \times 2) + (32 \times 3) + (16 \times 12) \][/tex]

Sagot :

GinnyAnswer
Certainly! Let's solve the problem step-by-step to find out the percentage by mass of aluminium in aluminium sulphate, [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex].

### Step 1: Determine the Atomic Masses
The atomic masses given in the question are:
- Aluminium (Al): 27 g/mol
- Sulphur (S): 32 g/mol
- Oxygen (O): 16 g/mol

### Step 2: Determine the Molecular Formula of Aluminium Sulphate
The molecular formula for aluminium sulphate is [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex].

### Step 3: Calculate the Molar Mass of Aluminium Sulphate
To find the molar mass of [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex], we need to sum the atomic masses of all atoms in the formula:
- Aluminium: There are 2 atoms of Al, so [tex]\( 2 \times 27 = 54 \)[/tex] g/mol.
- Sulphur: There are 3 atoms of S, so [tex]\( 3 \times 32 = 96 \)[/tex] g/mol.
- Oxygen: Each [tex]\( \text{SO}_4 \)[/tex] unit contains 4 atoms of O and there are 3 [tex]\( \text{SO}_4 \)[/tex] units. So, [tex]\( 4 \times 3 = 12 \)[/tex] atoms of O in total. Therefore, [tex]\( 12 \times 16 = 192 \)[/tex] g/mol.

Adding these together, we get the molar mass of [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex]:
[tex]\[ 54 \text{ (from Al)} + 96 \text{ (from S)} + 192 \text{ (from O)} = 342 \text{ g/mol} \][/tex]

### Step 4: Calculate the Mass Contribution of Aluminium
The mass of aluminium in one mole of [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex] is:
[tex]\[ 2 \times 27 \, \text{g} = 54 \, \text{g} \][/tex]

### Step 5: Calculate the Percentage by Mass of Aluminium
To find the percentage by mass of aluminium in the compound, we use the formula:
[tex]\[ \text{Percentage of Al} = \left( \frac{\text{Mass of Al}}{\text{Molar mass of } \text{Al}_2(\text{SO}_4)_3} \right) \times 100 \% \][/tex]
Substitute the values:
[tex]\[ \text{Percentage of Al} = \left( \frac{54 \, \text{g}}{342 \, \text{g/mol}} \right) \times 100 \% \approx 15.79 \% \][/tex]

Thus, the percentage by mass of aluminium in aluminium sulphate [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex] is approximately 15.79%.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.