Question

how many molecules are in 25.5g of iron (iii) hydroxide?

Answer 1

To calculate the number of molecules in 25.5 grams of iron (III) hydroxide, we first need to establish its chemical formula and molar mass:

The chemical formula for iron (III) hydroxide is \( \text{Fe(OH)}_3 \).

### Step 1: Calculate the molar mass of \( \text{Fe(OH)}_3 \)

- The molar mass of Iron (Fe) = 55.85 g/mol
- The molar mass of Oxygen (O) = 16.00 g/mol
- The molar mass of Hydrogen (H) = 1.01 g/mol

Now, calculate the molar mass of \( \text{Fe(OH)}_3 \):
\[
\text{Molar mass of Fe(OH)}_3 = 55.85\, \text{g/mol} + 3 \times (16.00\, \text{g/mol} + 1.01\, \text{g/mol})
\]
\[
= 55.85\, \text{g/mol} + 3 \times 17.01\, \text{g/mol}
\]
\[
= 55.85\, \text{g/mol} + 51.03\, \text{g/mol}
\]
\[
= 106.88\, \text{g/mol}
\]

### Step 2: Calculate the number of moles in 25.5 grams of \( \text{Fe(OH)}_3 \)

Now, we can convert grams to moles using the molar mass:
\[
\text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}
\]
\[
\text{Number of moles} = \frac{25.5\, \text{g}}{106.88\, \text{g/mol}} \approx 0.238\, \text{moles}
\]

### Step 3: Calculate the number of molecules

To find the number of molecules, we use Avogadro's number (\( 6.022 \times 10^{23} \) molecules/mol):
\[
\text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number}
\]
\[
\text{Number of molecules} = 0.238\, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mol}
\]
\[
\approx 1.43 \times 10^{23} \, \text{molecules}
\]

### Conclusion
There are approximately \( 1.43 \times 10^{23} \) molecules in 25.5 grams of iron (III) hydroxide.