How many grams of sodium hydroxide (NaOH) are required to prepare 250. mL of a 7.80 M solution?

• A. 78.0 g
• B. 78.0 mg
• C. 78.0 g
• D. 78.5 g

Answer: (C)

Verified step by step guidance

1. Identify the given information: volume of solution (V) = 250. mL and molarity (M) = 7.80 M. Remember to convert volume from milliliters to liters because molarity is in moles per liter.
2. Convert the volume from milliliters to liters using the conversion factor: \$1\, \text{L} = 1000\, \text{mL}\(. So, \)V (\text{L}) = \frac{250.\, \text{mL}}{1000}$.
3. Use the definition of molarity to find the number of moles of NaOH needed: \(M = \frac{\text{moles of solute}}{\text{liters of solution}}\). Rearranged, this is \(\text{moles of NaOH} = M \times V (\text{L})\).
4. Calculate the mass of NaOH required by converting moles to grams using the molar mass of NaOH. The molar mass of NaOH is calculated by adding the atomic masses: Na (22.99 g/mol) + O (16.00 g/mol) + H (1.01 g/mol). Then, \(\text{mass} = \text{moles} \times \text{molar mass}\).
5. Combine all the steps to find the mass of NaOH needed to prepare the solution. This mass will be the amount of NaOH in grams required to make 250 mL of a 7.80 M solution.