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 .
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To calculate the mole fraction of NaOH in the diluted solution, we need to determine the number of moles of NaOH and the total number of moles in the solution.
First, let's find the number of moles of NaOH in 100g of solution.
Given:
Mass of water = 100g
Density of NaOH = 1.08g/ml
Since we are given the density of NaOH, we can assume that the 10.6M concentration refers to moles of NaOH per liter of solution (mol/L). So, we need to convert the 100g of water to milliliters (ml).
The volume of water = mass / density = 100g / 1.08g/ml ≈ 92.6 ml
Now, we can calculate the number of moles of NaOH in 10.6M NaOH solution.
Molarity (M) = moles of solute / volume of solution in liters
10.6M = moles of NaOH / 1L
moles of NaOH = 10.6 mol
Since the solution is diluted by adding 100g of water, the total volume of the diluted solution is the volume of water added (100ml) plus the original volume of the NaOH solution.
Total volume of solution = 92.6 ml + 100 ml = 192.6 ml
Now, we can calculate the mole fraction of NaOH by dividing the moles of NaOH by the total moles in the solution.
Mole fraction of NaOH = moles of NaOH / total moles in solution
Mole fraction of NaOH = 10.6 mol / (10.6 mol + moles of water)
To find the moles of water, we need to convert the mass of water to moles. The molar mass of water (Hâ‚‚O) is approximately 18 g/mol.
Moles of water = mass of water / molar mass of water
Moles of water = 100g / 18 g/mol ≈ 5.56 mol
Now, we can substitute the values into the mole fraction equation.
Mole fraction of NaOH = 10.6 mol / (10.6 mol + 5.56 mol)
Mole fraction of NaOH ≈ 0.656
Therefore, the mole fraction of NaOH in the diluted solution is approximately 0.656.