To find the molar mass of magnesium hydroxide, [tex]\( \text{Mg(OH)}_2 \)[/tex], let's follow these steps:
1. Identify the atoms and their quantities in the compound:
- Magnesium (Mg): 1 atom
- Oxygen (O): 2 atoms
- Hydrogen (H): 2 atoms
2. Find the atomic masses of each element:
- The atomic mass of Magnesium (Mg) is 24.305 g/mol.
- The atomic mass of Oxygen (O) is 15.999 g/mol.
- The atomic mass of Hydrogen (H) is 1.008 g/mol.
3. Calculate the total mass contributed by each element in the compound:
- For Magnesium: [tex]\( 1 \times 24.305 \, \text{g/mol} \)[/tex]
- For Oxygen: [tex]\( 2 \times 15.999 \, \text{g/mol} \)[/tex]
- For Hydrogen: [tex]\( 2 \times 1.008 \, \text{g/mol} \)[/tex]
4. Add the masses contributed by each element to get the molar mass of [tex]\( \text{Mg(OH)}_2 \)[/tex]:
- Molar mass of [tex]\( \text{Mg(OH)}_2 \)[/tex] = [tex]\( 24.305 \, \text{g/mol} + 2 \times (15.999 \, \text{g/mol} + 1.008 \, \text{g/mol}) \)[/tex]
5. Perform the addition:
- Calculate the contribution of Oxygen and Hydrogen together for one [tex]\( \text{OH} \)[/tex] group: [tex]\( 15.999 \, \text{g/mol} + 1.008 \, \text{g/mol} = 17.007 \, \text{g/mol} \)[/tex]
- Since there are two [tex]\( \text{OH} \)[/tex] groups, multiply by 2: [tex]\( 2 \times 17.007 \, \text{g/mol} = 34.014 \, \text{g/mol} \)[/tex]
- Now, add the Magnesium mass: [tex]\( 24.305 \, \text{g/mol} + 34.014 \, \text{g/mol} = 58.319 \, \text{g/mol} \)[/tex]
Therefore, the molar mass of magnesium hydroxide, [tex]\( \text{Mg(OH)}_2 \)[/tex], is [tex]\( 58.319 \, \text{g/mol} \)[/tex].
