To determine the molarity of the given aqueous solution with the provided amount of [tex]$C_6H_{12}O_6$[/tex] (glucose), we follow these steps:
### Step-by-Step Solution
1. Understanding the Problem:
- We are given the number of moles of solute ([tex]$C_6H_{12}O_6$[/tex]) and the volume of the solution.
- Our task is to find the molarity, which is defined as the number of moles of solute per liter of solution.
2. Given Values:
- Moles of [tex]$C_6H_{12}O_6$[/tex]: [tex]\(2.90 \, \text{mol}\)[/tex]
- Volume of the solution: [tex]\(0.700 \, \text{L}\)[/tex]
3. Formula for Molarity:
Molarity (M) is given by the formula:
[tex]\[
\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
\][/tex]
4. Plug in the Given Values:
[tex]\[
\text{Molarity (M)} = \frac{2.90 \, \text{mol}}{0.700 \, \text{L}}
\][/tex]
5. Perform the Calculation:
[tex]\[
\text{Molarity (M)} = \frac{2.90}{0.700} = 4.142857142857143
\][/tex]
6. Significant Figures:
- The number of significant figures in the given values dictates the number of significant figures in the final answer.
- [tex]\(2.90\)[/tex] has 3 significant figures.
- [tex]\(0.700\)[/tex] also has 3 significant figures.
- Therefore, our final answer for molarity should be rounded to 3 significant figures.
7. Rounded Answer:
[tex]\[
\text{Molarity (M)} \approx 4.14 \, \text{M}
\][/tex]
8. Expressing the Answer in Scientific Notation (if necessary):
- Since [tex]\(4.14\)[/tex] is not an exponential number, express it in standard form is sufficient.
9. Final Answer:
[tex]\[
4.14 \, \text{M}
\][/tex]
### Summary:
The molarity of the solution containing [tex]\(2.90 \, \text{mol}\)[/tex] of [tex]\(C_6H_{12}O_6\)[/tex] in [tex]\(0.700 \, \text{L}\)[/tex] of solution is [tex]\(4.14 \, \text{M}\)[/tex] with the correct number of significant figures.
