Please show me step by step. Thank you.
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 neutralize a 20.0-mL sample of NaOH solution. What is the concentration of the NaOH solution?
2NaOH + H2SO4 ==> Na2SO4 + 2H2O
mols H2SO4 = M x L = about 0.02 but that's only approximate. The look at the equation; mols NaOH = twice that or about 0.05 mols in the 20.00 mL (20.00 mL = 0.02L)
So (NaOH) = about 0.05mol/0.02L = ?M
To find the concentration of the NaOH solution, we can use the stoichiometry of the neutralization reaction between NaOH and H2SO4. Here's how you can solve it step by step:
Step 1: Write the balanced chemical equation for the reaction between NaOH and H2SO4:
NaOH + H2SO4 -> Na2SO4 + H2O
Step 2: Identify the mole ratio between NaOH and H2SO4 from the balanced equation:
From the equation, we can see that 1 mole of NaOH reacts with 1 mole of H2SO4.
Step 3: Calculate the number of moles of H2SO4 used:
We know that the volume of the H2SO4 solution used is 45.7 mL, and the concentration is 0.500 M. The formula for calculating moles is:
Moles = Concentration (M) x Volume (L)
Convert the volume to liters:
Volume = 45.7 mL = 45.7 mL x (1 L / 1000 mL) = 0.0457 L
Now calculate the number of moles:
Moles of H2SO4 = 0.500 M x 0.0457 L = 0.02285 moles
Step 4: Calculate the number of moles of NaOH used:
Since the mole ratio between NaOH and H2SO4 is 1:1, the number of moles of NaOH used is also 0.02285 moles.
Step 5: Calculate the concentration of the NaOH solution:
Now we know that the number of moles of NaOH used is 0.02285 moles, and the volume of the NaOH solution used is 20.0 mL. Convert the volume to liters:
Volume = 20.0 mL = 20.0 mL x (1 L / 1000 mL) = 0.0200 L
The formula for calculating concentration is:
Concentration (M) = Moles / Volume
Concentration of the NaOH solution = 0.02285 moles / 0.0200 L = 1.143 M
Therefore, the concentration of the NaOH solution is 1.143 M.