How many grams of sucrose are needed to make a 375 millimolar concentration in 250milliliters
The correct answer and explanation is:
To find the grams of sucrose needed to make a 375 millimolar (mM) solution in 250 milliliters (mL), we use the molarity formula: Molarity (M)=moles of soluteliters of solution\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}}
Since we’re given millimolar (mM), we’ll convert it to molar (M): 375 mM=0.375 M375 \, \text{mM} = 0.375 \, \text{M}
We’re also given volume in mL, so convert to liters: 250 mL=0.250 L250 \, \text{mL} = 0.250 \, \text{L}
Now calculate moles of sucrose: Moles=Molarity×Volume=0.375 mol/L×0.250 L=0.09375 mol\text{Moles} = Molarity \times Volume = 0.375 \, \text{mol/L} \times 0.250 \, \text{L} = 0.09375 \, \text{mol}
Next, convert moles to grams using the molar mass of sucrose (C₁₂H₂₂O₁₁), which is approximately 342.3 g/mol: Mass (g)=Moles×Molar Mass=0.09375×342.3=32.093 g\text{Mass (g)} = \text{Moles} \times \text{Molar Mass} = 0.09375 \times 342.3 = 32.093 \, \text{g}
✅ Final Answer:
32.09 grams of sucrose are needed to make a 375 mM solution in 250 mL of water.
🔍 Explanation (300 words):
Creating a solution of a specific molarity involves using the formula: Molarity=Moles of soluteLiters of solution\text{Molarity} = \frac{\text{Moles of solute}}{\text{Liters of solution}}
Molarity (M) tells us how many moles of solute are present in one liter of solution. In this case, we’re making a 375 mM (millimolar) solution, which is equal to 0.375 M. We’re preparing 250 mL of this solution, which is 0.250 liters. To determine the number of moles needed, multiply molarity by volume: Moles=0.375×0.250=0.09375 mol\text{Moles} = 0.375 \times 0.250 = 0.09375 \text{ mol}
Sucrose’s molar mass (its weight per mole) is 342.3 g/mol. This value is found by adding the atomic weights of its atoms:
12 Carbon (12×12.01), 22 Hydrogen (22×1.008), and 11 Oxygen (11×16.00).
Now, convert moles to grams: Grams=Moles×Molar Mass=0.09375×342.3=32.09 g\text{Grams} = \text{Moles} \times \text{Molar Mass} = 0.09375 \times 342.3 = 32.09 \text{ g}
Thus, to make the solution, you would weigh out 32.09 grams of sucrose, then dissolve it in water and make up the volume to 250 mL. This is a common technique in labs for preparing standard solutions used in biology, chemistry, and medical fields.