Sure, let's go through the detailed steps to complete the unit conversion setup using dimensional analysis for determining the moles of NaCl.
### Initial Information:
- Molecular weight of NaCl: [tex]\( 58.5 \, \text{g/mol} \)[/tex]
- Weight of the salt: [tex]\( 6.37 \, \text{g} \)[/tex]
We need to determine how many moles of NaCl are in 6.37 grams of salt.
### Calculation using Dimensional Analysis:
To find the number of moles, we will use the formula:
[tex]\[ \text{Moles of NaCl} = \frac{\text{Weight of salt}}{\text{Molecular weight of NaCl}} \][/tex]
### Filling in the Dimensional Analysis Setup:
1. A – The given weight of salt in grams.
2. B – The unit of weight we're given, which is grams.
3. C – The molecular weight of NaCl in grams per mole.
So, substituting the values here:
[tex]\[ A = 6.37 \, \text{g} \][/tex]
[tex]\[ B = 1 \, \text{g} \][/tex]
[tex]\[ C = 58.5 \, \text{g/mol} \][/tex]
### Verification of the Unit Conversion Setup:
To use dimensional analysis correctly:
[tex]\[
\text{Moles NaCl} = A \times \frac{B}{C}
\][/tex]
Substituting these values:
[tex]\[
\text{Moles NaCl} = 6.37 \, \text{g} \times \frac{1 \, \text{g}}{58.5 \, \text{g/mol}}
\][/tex]
This indeed simplifies to calculating the moles of NaCl:
[tex]\[
\text{Moles NaCl} = \frac{6.37}{58.5} = 0.1088888888888889
\][/tex]
### Conclusion:
Therefore,
[tex]\[ A = 6.37 \, \text{g} \][/tex]
[tex]\[ B = 1 \, \text{g} \][/tex]
[tex]\[ C = 58.5 \, \text{g/mol} \][/tex]
And the number of moles of NaCl is approximately 0.1089 moles.
So, completing the setup:
[tex]\[
A \times \frac{B}{C} = \text{Moles of NaCl}
\][/tex]
where:
[tex]\[
A = 6.37
\][/tex]
[tex]\[
B = 1 \, \text{g}
\][/tex]
[tex]\[
C = 58.5 \, \text{g/mol}
\][/tex]
