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Chapter 12: Problem 15

How many milliliters of a 2.55 M solution of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), molar mass \(=180.155 \mathrm{~g} / \mathrm{mol}\), do you need to obtain \(25.0 \mathrm{~g}\) of glucose?

Short Answer

Expert verified
To obtain $25.0 \text{ g}$ of glucose from a $2.55 \text{ M}$ solution, you will need a volume of \( \frac{\frac{25.0 \text{ g}}{180.155 \text{ g/mol}}}{2.55 \text{ M}} \) × 1000 mL.

Step by step solution

01

Calculate moles of glucose

To find the moles of glucose, we will use the formula: moles = mass / molar mass Given mass of glucose = 25.0 g Molar mass of glucose = 180.155 g/mol So, moles of glucose = \( \frac{25.0 \text{ g}}{180.155 \text{ g/mol}} \)
02

Calculate the volume of the solution

Now, we have the moles of glucose and the molarity of the solution. We will use the formula of molarity to find the volume of the solution in liters: Molarity (M) = moles of solute / volume of solution (in liters) Given molarity of the solution = 2.55 M Substituting the values in the equation: 2.55 M = \( \frac{moles \, of \, glucose}{volume \, of \, solution} \) Solving for the volume of the solution, we get: volume of solution = \( \frac{moles \, of \, glucose}{2.55 \text{ M}} \)
03

Convert volume to milliliters

Since 1 liter = 1000 milliliters (mL), we will convert the volume of solution (in liters) that we found in step 2 to milliliters. volume of solution (in milliliters) = volume of solution (in liters) × 1000 Now, we have all the necessary information to find the required volume of the glucose solution: volume of solution (in milliliters) = \( \frac{moles \, of \, glucose}{2.55 \text{ M}} \) × 1000 Putting the values from step 1, we get: volume of solution (in milliliters) = \( \frac{\frac{25.0 \text{ g}}{180.155 \text{ g/mol}}}{2.55 \text{ M}} \) × 1000 Calculate the above expression to get the required volume of the solution.

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