100g of water is added into 10.6M NaOH solution. The diluted NaOH then neutralized completely with H2SO4 . density of NaOH is 1.08g/ml . calculate the mole fraction of NaOH in diluted solution .
Adding 100-g HOH = 100-ml HOH into 10.6-M NaOH => 10.6 mole/Liter + 0.100L HOH => 10.6 mole NaOH/1.10 Liters Solution => 9.64 Molar in NaOH.
H2SO4 + 2NaOH => Na2SO4 + 2HOH
1/2(9.64M) H2SO4 + 9.64M NaOH => 1/2(Na2SO4) + HOH
=> (4.82mol/L)H2SO4 + (9.64mol/L)NaOH
=> Neutral Solution.
Using moles H2SO4 = 4.82 mole, and
moles of NaOH = 9.64 ... The mole fraction can be computed as follows...
X(NaOH) = 9.64 mole / (4.82 + 9.64) total moles = 0.6667 mole fraction NaOH ...
X(Na2SO4) = 4.82 mole / (4.82 + 9.64) total moles = 0.3333 mole fraction Na2SO4
Sum mole fractions = 1 = 0.6667NaOH + 0.3333Na2SO4.
To calculate the mole fraction of NaOH in the diluted solution, we need to first determine the number of moles of NaOH added to the solution and the final volume of the solution.
Step 1: Calculate the number of moles of NaOH added.
The molar mass of NaOH is 22.99 g/mol for sodium (Na), 16.00 g/mol for oxygen (O), and 1.01 g/mol for hydrogen (H).
NaOH molar mass = 22.99 + 16.00 + 1.01 = 40.00 g/mol
Given that we added 100 g of water to the solution, we can calculate the number of moles of NaOH added:
moles of NaOH = mass of NaOH / molar mass of NaOH
= 100 g / 40.00 g/mol
= 2.5 moles
Step 2: Calculate the final volume of the solution.
The density of NaOH is given as 1.08 g/mL. By using the density and mass of the solution, we can determine the volume of the solution.
volume of solution = mass of solution / density of solution
= (100 g + mass of NaOH) / 1.08 g/mL
Since the density is given in grams per milliliter and the mass of NaOH is given in grams, we can assume that the volume doesn't change significantly upon adding NaOH. Therefore, the volume of the solution is approximately equal to the volume of the water added, which is 100 mL.
Step 3: Calculate the mole fraction of NaOH.
The mole fraction of a component in a solution is the ratio of the number of moles of that component to the total number of moles in the solution.
moles of water (H2O) = volume of water (in liters) * density of water (g/ml) / molar mass of water (g/mol)
= 100 mL * 1 g/mL / 18.01 g/mol
= 5.55 moles
Total moles in the solution = moles of NaOH + moles of water
= 2.5 moles + 5.55 moles
= 8.05 moles
Mole fraction of NaOH = moles of NaOH / total moles in the solution
= 2.5 moles / 8.05 moles
≈ 0.3104
Therefore, the mole fraction of NaOH in the diluted solution is approximately 0.3104.