Let's solve the given problem step by step.
We have the following values:
- Weight: [tex]\( 60.7 \, \text{grams} \)[/tex]
- Volume conversion factor: [tex]\( 10^{-3} \, \text{liters per milliliter} \)[/tex]
- Molar mass: [tex]\( 116.74 \, \text{grams per mole} \)[/tex]
- Molarity: [tex]\( 3.7 \, \text{moles per liter} \)[/tex]
We need to calculate the expression:
[tex]\[
\frac{(60.7 \, \text{g})\left(\frac{1 \, \text{mL}}{10^{-3} \, \text{L}}\right)}{\left(116.74 \, \frac{\text{g}}{\text{mol}}\right)\left(3.7 \, \frac{\text{mol}}{\text{L}}\right)}
\][/tex]
1. Convert the weight from grams to liters:
Given the volume conversion factor [tex]\( 10^{-3} \, \text{liters} \)[/tex], we can convert the weight in grams to volume in liters by multiplying:
[tex]\[
60.7 \, \text{g} \times 10^{-3} \, \frac{\text{L}}{\text{mL}} = 60.7 \times 10^{-3} \, \text{L} = 0.0607 \, \text{L}
\][/tex]
So, the volume in liters is [tex]\( 0.0607 \, \text{L} \)[/tex].
2. Calculate the denominator:
The denominator is the product of the molar mass and the molarity:
[tex]\[
(116.74 \, \text{g/mol}) \times (3.7 \, \text{mol/L}) = 116.74 \times 3.7 = 431.938 \, \text{g·mol/L}
\][/tex]
3. Calculate the final result:
Now we need to divide the volume in liters by the denominator:
[tex]\[
\frac{0.0607 \, \text{L}}{431.938 \, \text{g/mol·L}} = 0.00014052942783455034
\][/tex]
Thus, the final result of the given expression is approximately [tex]\( 0.00014052942783455034 \)[/tex].
