To determine the percent composition of [tex]\( \text{Ca(OH)}_2 \)[/tex], we need to start by analyzing its chemical structure and calculating the molar masses of its individual components.
Here are the step-by-step calculations:
1. Identify the Molar Masses of the Elements:
- Calcium (Ca): [tex]\(40.08 \, \text{g/mol}\)[/tex]
- Oxygen (O): [tex]\(16.00 \, \text{g/mol}\)[/tex]
- Hydrogen (H): [tex]\(1.01 \, \text{g/mol}\)[/tex]
2. Calculate the Molar Mass of [tex]\( \text{Ca(OH)}_2 \)[/tex]:
[tex]\( \text{Ca(OH)}_2 \)[/tex] contains:
- 1 Calcium atom: [tex]\(40.08 \, \text{g/mol}\)[/tex]
- 2 Oxygen atoms: [tex]\(16.00 \, \text{g/mol} \times 2 = 32.00 \, \text{g/mol}\)[/tex]
- 2 Hydrogen atoms: [tex]\(1.01 \, \text{g/mol} \times 2 = 2.02 \, \text{g/mol}\)[/tex]
Therefore, the total molar mass of [tex]\( \text{Ca(OH)}_2 \)[/tex] is:
[tex]\[
40.08 \, \text{g/mol} + 32.00 \, \text{g/mol} + 2.02 \, \text{g/mol} = 74.10 \, \text{g/mol}
\][/tex]
3. Calculate the Percent Composition of Each Element:
- Calcium (Ca):
[tex]\[
\text{Percent of Ca} = \frac{40.08 \, \text{g/mol}}{74.10 \, \text{g/mol}} \times 100\% = 54.09\%
\][/tex]
- Oxygen (O):
[tex]\[
\text{Percent of O} = \frac{32.00 \, \text{g/mol}}{74.10 \, \text{g/mol}} \times 100\% = 43.19\%
\][/tex]
- Hydrogen (H):
[tex]\[
\text{Percent of H} = \frac{2.02 \, \text{g/mol}}{74.10 \, \text{g/mol}} \times 100\% = 2.73\%
\][/tex]
Rounding these values to one decimal place, we get:
- Percent composition of Calcium ([tex]\( \text{Ca} \)[/tex]): [tex]\(54.1\%\)[/tex]
- Percent composition of Oxygen ([tex]\( \text{O} \)[/tex]): [tex]\(43.2\%\)[/tex]
- Percent composition of Hydrogen ([tex]\( \text{H} \)[/tex]): [tex]\(2.7\%\)[/tex]
4. Comparing with the Given Options:
Let's look at the percent compositions provided in the options:
[tex]\[
\begin{array}{l}
\text{Option 1: } 37.7\% \, \text{Ca} , 53.0\% \, \text{O} , 10.3\% \, \text{H} \\
\text{Option 2: } 45.5\% \, \text{Ca} , 38.2\% \, \text{O} , 16.3\% \, \text{H} \\
\text{Option 3: } 54.0\% \, \text{Ca} , 43.0\% \, \text{O} , 2.7\% \, \text{H} \\
\text{Option 4: } 64.7\% \, \text{Ca} , 27.0\% \, \text{O} , 8.3\% \, \text{H} \\
\end{array}
\][/tex]
The third option ([tex]\(54.0\% \, \text{Ca}, 43.0\% \, \text{O}, 2.7\% \, \text{H} \)[/tex]) matches our calculated percent compositions very closely.
Therefore, the correct answer is:
[tex]\[
\boxed{54.0\% \, \text{Ca}, 43.0\% \, \text{O}, 2.7\% \, \text{H}}
\][/tex]
