One commercial method used to peel potatoes is to soak them in a solution of NaOH for a short time, remove them from the NaOH, and spray off the peel. The concentration of NaOH is normally in the range of 3 to 6 M. The NaOH is analyzed periodically. In one such analysis, 45.7 mL of 0.500 M H2SO4 is required to react completely with a 12.5 mL sample of NaOH solution. What is the concentration of the NaOH solution?

2NaOH + H2SO4 ==> Na2SO4 + 2H2O

moles H2SO4 = M x L
moles NaOH (from the equation) = 1/2 moles H2SO4
M NaOH = moles NaOH/L NaOH = ??

4.78

To determine the concentration of the NaOH solution, you can use the concept of stoichiometry. Here's how you can approach the problem step by step:

1. Write the balanced chemical equation for the reaction between NaOH and H2SO4:
NaOH + H2SO4 -> Na2SO4 + H2O

2. Determine the mole-to-mole ratio between NaOH and H2SO4 from the balanced equation. In this case, the ratio is 1:1. This means that 1 mole of NaOH reacts with 1 mole of H2SO4.

3. Use the given information about the volume and concentration of H2SO4 to calculate the number of moles of H2SO4 used. The volume of the H2SO4 solution is 45.7 mL, and the concentration is 0.500 M (moles per liter). Convert the volume to liters by dividing by 1000:
Moles of H2SO4 = Volume (L) x Concentration (M)

Moles of H2SO4 = (45.7 mL / 1000 mL/L) x 0.500 M

4. The moles of H2SO4 used in the reaction will be equal to the moles of NaOH since they have a 1:1 ratio.

5. Calculate the number of moles of NaOH:
Moles of NaOH = Moles of H2SO4

6. Determine the volume of the NaOH solution used in the reaction, which is given as 12.5 mL. Convert the volume to liters:
Volume of NaOH solution (L) = 12.5 mL / 1000 mL/L

7. Calculate the concentration of the NaOH solution using the moles of NaOH and the volume of the solution:
Concentration (M) = Moles / Volume (L)

Now you have all the information needed to solve the problem. Plug in the values you obtained and calculate the concentration of the NaOH solution.

1.41