To determine how many grams are in [tex]\( 9.28 \times 10^{23} \)[/tex] molecules of NaCl, we need to follow a series of steps. Here’s the detailed, step-by-step solution:
1. Understand the Given Data and Constants:
- Number of NaCl molecules ([tex]\( N \)[/tex]) = [tex]\( 9.28 \times 10^{23} \)[/tex]
- Molar mass of NaCl ([tex]\( M \)[/tex]) = 58.44 grams per mole
- Avogadro's number ([tex]\( N_A \)[/tex]) = [tex]\( 6.02 \times 10^{23} \)[/tex] molecules per mole
2. Convert Molecules to Moles:
First, we need to convert the given number of molecules to moles. One mole of any substance contains Avogadro's number of molecules.
[tex]\[
\text{Moles of NaCl} = \frac{\text{Number of molecules}}{\text{Avogadro's number}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Moles of NaCl} = \frac{9.28 \times 10^{23} \text{ molecules}}{6.02 \times 10^{23} \text{ molecules per mole}}
\][/tex]
This simplifies approximately to:
[tex]\[
\text{Moles of NaCl} \approx 1.5415282392026577 \text{ moles}
\][/tex]
3. Convert Moles to Grams:
Now that we know the number of moles, we convert moles to grams using the molar mass of NaCl.
[tex]\[
\text{Mass (in grams)} = \text{Moles} \times \text{Molar Mass}
\][/tex]
Substituting in the known values:
[tex]\[
\text{Mass (in grams)} = 1.5415282392026577 \text{ moles} \times 58.44 \text{ grams per mole}
\][/tex]
This gives a result of:
[tex]\[
\text{Mass (in grams)} \approx 90.0869102990033 \text{ grams}
\][/tex]
Therefore, there are approximately 90.09 grams in [tex]\( 9.28 \times 10^{23} \)[/tex] molecules of NaCl.
