To solve for the molar mass of the compound [tex]\(M(OH)_2\)[/tex], we need to follow these steps:
1. Identify the atomic masses:
- The atomic mass of element [tex]\(M\)[/tex] is given as 55.85 amu.
- The atomic mass of oxygen (O) is 16.00 amu.
- The atomic mass of hydrogen (H) is 1.01 amu.
2. Determine the composition of [tex]\(M(OH)_2\)[/tex]:
- The compound [tex]\(M(OH)_2\)[/tex] indicates that there is one atom of [tex]\(M\)[/tex], two atoms of oxygen (O), and two atoms of hydrogen (H).
3. Calculate the molar mass of the compound:
- The molar mass is calculated by summing the atomic masses of all the atoms in the compound.
[tex]\[
\text{Molar mass of } M(OH)_2 = \text{atomic mass of } M + 2 \times (\text{atomic mass of } O + \text{atomic mass of } H)
\][/tex]
Plugging in the values, we get:
[tex]\[
\text{Molar mass of } M(OH)_2 = 55.85 + 2 \times (16.00 + 1.01)
\][/tex]
[tex]\[
= 55.85 + 2 \times 17.01
\][/tex]
[tex]\[
= 55.85 + 34.02
\][/tex]
[tex]\[
= 89.87 \text{ g/mol}
\][/tex]
So, the molar mass of the compound [tex]\(M(OH)_2\)[/tex] is 89.87 g/mol.
Given the options:
- 104.86 g
- 72.86 g
- 74.88 g
- 89.87 g
- 106.87 g
The correct answer is 89.87 g.
