To calculate the molarity (M) of the solution, we can use the following formula:
\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \]
First, we need to convert grams of table sugar (C₁₂H₂₂O₁₁) to moles.
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Calculate the molar mass of C₁₂H₂₂O₁₁:
- Carbon (C): 12.01 g/mol × 12 = 144.12 g/mol
- Hydrogen (H): 1.008 g/mol × 22 = 22.176 g/mol
- Oxygen (O): 16.00 g/mol × 11 = 176.00 g/mol
- Total = 144.12 + 22.176 + 176.00 = 342.296 g/mol
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Calculate the moles of table sugar in 10.0 grams: \[ \text{moles of C}{12}\text{H}{22}\text{O}_{11} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} = \frac{10.0 \text{ g}}{342.296 \text{ g/mol}} \approx 0.0292 \text{ moles} \]
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Convert 50.0 mL to liters: \[ 50.0 \text{ mL} = 0.0500 \text{ L} \]
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Now calculate the molarity: \[ \text{Molarity (M)} = \frac{0.0292 \text{ moles}}{0.0500 \text{ L}} \approx 0.584 \text{ M} \]
Thus, the correct answer is: b. 0.584 M