Final answer:
To find the moles of NaOH added, the mass of NaOH is divided by its molar mass and then adjusted for the solution's molarity and density. The volume of NaOH solution is found using mass and density, and then moles are calculated using this volume and molarity. The result is approximately 0.214 moles of NaOH.
Step-by-step explanation:
To calculate how many moles of NaOH were added, we need to use the mass of NaOH and its molar mass. The molar mass of NaOH is approximately 40 g/mol. So, we divide the mass of NaOH by its molar mass to find the number of moles:
Moles of NaOH = mass of NaOH ÷ molar mass of NaOH = 12.221g ÷ 40 g/mol = 0.3055 moles.
However, we are given the concentration of the NaOH solution as 18.2 M, which indicates that the NaOH used was not in its pure form but rather in a solution.
We need to consider the concentration and density to find the exact moles of NaOH in the solution. Since we have the mass and density of the solution (1.00 g/mL), we can first find the volume of the NaOH solution using the mass.
The volume of NaOH solution is equal to its mass divided by the density.
Volume of NaOH solution = mass of NaOH solution ÷ density = 12.221g ÷ 1.00 g/mL = 12.221 mL.
Now, convert this volume to liters to use it with molarity (M):
Volume in liters = 12.221 mL ÷ 1000 mL/L = 0.012221 L.
Finally, calculate the moles of NaOH from the volume and molarity:
Moles of NaOH = volume in liters × molarity = 0.012221 L × 18.2 M = 0.2224 moles.
The correct answer is thus closest to option c) 0.214 moles, as it is the value that most closely approximates our calculated number of moles.