1. 4 mL of NaOH must be mixed with 96 mL water to obtain 100 mL of NaOH in a 0.02M solution.
2. The molar fraction of NaOH is ≈ 0.67
3. The molar fraction of Water is ≈ 0.33
Explanation:
To determine the volumes of water and 0.5 M NaOH needed to make a 100 mL solution of NaOH with a concentration of 0.02 M, we can use the formula: [tex]M_{1} V_{1} =M_{2} V_{2}[/tex]
Setup:
[tex]\[ (0.5 \, M) \cdot V_1 = (0.02 \, M) \cdot (100 \, mL) \]\\ V_1 = \frac{(0.02 \, M) (100 \, mL)}{0.5 \, M} \] \\V_1 = \frac{2 \, mL}{0.5 \, M} \]\\ V_1 = 4 \, mL \][/tex]
So now we have the volume of NaOH needed to mix with water in a 0.5 M solution.
Let's calculate molar fractions by using the molarities:
[tex]moles = concentration (M) \times volume (L)\\moles~of~NaOH = 0.02 \, M \times 0.1 \, L \quad (100 \, mL = 0.1 \, L) = 0.002 \, moles\\moles~of~H2O = 0.5 \, M \times 0.002 \, L \quad (2 \, mL = 0.002 \, L) = 0.001 \, moles\:\\_{\text{NaOH}} = \frac{0.002 \, \text{moles}}{0.002 \, \text{moles} + 0.001 \, \text{moles}} = 0.67[/tex]
Subtract the molar fraction of NaOH by 1 to get the value of water:
[tex]1-0.67 = 0.33[/tex]
So the molar fraction for NaOH is 0.67, and the molar fraction for water is 0.33
That's it!
