How many grams of NaOH are required to prepare 240 mL of a 3.50 M NaOH solution? How many grams of NaOH are required to prepare 240 mL of a 3.50 M NaOH solution? 0.840 g 33.6 g 54.8 g 583 g
The Correct Answer and Explanation is:
To solve this, we will use the relationship between molarity, volume, and moles, which is given by the formula:Molarity (M)=moles of solutevolume of solution in liters\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}Molarity (M)=volume of solution in litersmoles of solute
Step 1: Find the moles of NaOH needed.
We know the molarity of the NaOH solution is 3.50 M (moles per liter), and the volume required is 240 mL. First, we convert the volume from milliliters to liters:240 mL=0.240 L240 \, \text{mL} = 0.240 \, \text{L}240mL=0.240L
Now, use the molarity formula to find the moles of NaOH:moles of NaOH=Molarity×Volume\text{moles of NaOH} = \text{Molarity} \times \text{Volume}moles of NaOH=Molarity×Volumemoles of NaOH=3.50 M×0.240 L\text{moles of NaOH} = 3.50 \, \text{M} \times 0.240 \, \text{L}moles of NaOH=3.50M×0.240Lmoles of NaOH=0.84 moles\text{moles of NaOH} = 0.84 \, \text{moles}moles of NaOH=0.84moles
Step 2: Convert moles to grams.
Now, to convert moles of NaOH to grams, we need the molar mass of NaOH. The molar mass is the sum of the atomic masses of sodium (Na), oxygen (O), and hydrogen (H):Molar mass of NaOH=22.99 g/mol (Na)+15.999 g/mol (O)+1.008 g/mol (H)=39.997 g/mol\text{Molar mass of NaOH} = 22.99 \, \text{g/mol (Na)} + 15.999 \, \text{g/mol (O)} + 1.008 \, \text{g/mol (H)} = 39.997 \, \text{g/mol}Molar mass of NaOH=22.99g/mol (Na)+15.999g/mol (O)+1.008g/mol (H)=39.997g/mol
Now, calculate the mass in grams:Mass of NaOH=moles of NaOH×molar mass of NaOH\text{Mass of NaOH} = \text{moles of NaOH} \times \text{molar mass of NaOH}Mass of NaOH=moles of NaOH×molar mass of NaOHMass of NaOH=0.84 moles×39.997 g/mol\text{Mass of NaOH} = 0.84 \, \text{moles} \times 39.997 \, \text{g/mol}Mass of NaOH=0.84moles×39.997g/molMass of NaOH≈33.6 g\text{Mass of NaOH} \approx 33.6 \, \text{g}Mass of NaOH≈33.6g
Step 3: Conclusion.
The correct answer is 33.6 grams of NaOH required to prepare 240 mL of a 3.50 M NaOH solution.
Thus, the answer is 33.6 g.
