Sure! Let's go through a detailed, step-by-step solution for the given problem.
We need to compute the product of the molarity, the volume in liters, and the molar mass:
[tex]\[ \text{Molarity} = 1.8 \, \frac{\text{mol}}{\text{L}} \][/tex]
[tex]\[ \text{Volume} = 10^{-3} \, \text{L} \, (\text{conversion of 1 mL to L}) \][/tex]
[tex]\[ \text{Molar Mass} = 48.62 \, \frac{\text{g}}{\text{mol}} \][/tex]
The expression we need to evaluate is:
[tex]\[ \left(1.8 \frac{\text{mol}}{\text{L}}\right) \left( \frac{10^{-3} \, \text{L}}{1 \, \text{mL}} \right) \left( 48.62 \frac{\text{g}}{\text{mol}} \right) \][/tex]
Step-by-step, we follow these steps:
1. Multiply the Molarity and the Volume:
[tex]\[ 1.8 \, \frac{\text{mol}}{\text{L}} \times 10^{-3} \, \text{L} \][/tex]
This multiplication leads to:
[tex]\[ 1.8 \times 10^{-3} \frac{\text{mol}}{\text{L}} \times \text{L} = 1.8 \times 10^{-3} \, \text{mol} \][/tex]
2. Multiply the Resulting Value by the Molar Mass:
[tex]\[ 1.8 \times 10^{-3} \, \text{mol} \times 48.62 \, \frac{\text{g}}{\text{mol}} \][/tex]
3. When molarity is multiplied by volume and molar mass:
- The units of mol cancel, leaving us with the unit of grams.
- The numerical multiplication:
[tex]\[ 1.8 \times 10^{-3} \times 48.62 \][/tex]
4. Performing the final multiplication:
[tex]\[ 1.8 \times 48.62 = 87.516 \][/tex]
Then,
[tex]\[ 87.516 \times 10^{-3} = 0.087516 \][/tex]
Thus, the evaluated result of the entire expression is:
[tex]\[ \boxed{0.087516} \][/tex]
This is the final answer.
