To determine the number of molecules in a 23.45 g sample of copper(II) hydroxide, [tex]\( Cu(OH)_2 \)[/tex], we need to follow these steps:
1. Convert the mass of the sample to moles:
The molar mass of copper(II) hydroxide ([tex]\( Cu(OH)_2 \)[/tex]) is given as [tex]\( 97.562 \, \text{g/mol} \)[/tex]. This means that 1 mole of [tex]\( Cu(OH)_2 \)[/tex] weighs [tex]\( 97.562 \, \text{g} \)[/tex].
First, calculate the number of moles in a [tex]\( 23.45 \, \text{g} \)[/tex] sample using the relationship:
[tex]\[
\text{Number of moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}
\][/tex]
So,
[tex]\[
\text{Number of moles} = \frac{23.45 \, \text{g}}{97.562 \, \text{g/mol}} \approx 0.2404 \, \text{mol}
\][/tex]
2. Convert moles to molecules:
One mole of any substance contains Avogadro's number of molecules, which is [tex]\( 6.022 \times 10^{23} \)[/tex] molecules per mole.
To find the number of molecules in the given number of moles, use the relationship:
[tex]\[
\text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number}
\][/tex]
Thus,
[tex]\[
\text{Number of molecules} = 0.2404 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol}
\][/tex]
[tex]\[
\text{Number of molecules} \approx 1.447 \times 10^{23} \, \text{molecules}
\][/tex]
In conclusion, a 23.45 g sample of [tex]\( Cu(OH)_2 \)[/tex] contains approximately [tex]\( 0.2404 \, \text{moles} \)[/tex] and [tex]\( 1.447 \times 10^{23} \)[/tex] molecules of [tex]\( Cu(OH)_2 \)[/tex]. These results are expressed to the correct number of significant figures based on the given values in the problem.
