How is 50 ml of 20 millimolar (mM) sodium hydroxide (NaOH MW = 40) prepared? a. Mix 40g of NaOH and fill with water up to 50mL b. Mix 80mg of NaOH and fill with water up to 50mL c. Mix 80g of NaOH and fill with water up to 50mL d. Mix 40mg of NaOH and fill with water up to 50mL
The Correct Answer and Explanation is:
To prepare 50 mL of 20 millimolar (mM) sodium hydroxide (NaOH) solution, we can follow these steps:
Step 1: Understand the definition of millimolar concentration
- Millimolar (mM) refers to 1 millimole of solute in 1 liter of solution.
- Therefore, a 20 mM solution means 20 millimoles (mmol) of NaOH in 1 liter of solution.
Step 2: Calculate the amount of NaOH required
- First, calculate the number of moles of NaOH required for 50 mL of 20 mM solution.
- We know that 1 liter (L) = 1000 mL, and the solution is 20 mM, which is 20 millimoles per liter. The formula for moles is: moles of NaOH=concentration (mM)×volume (L)\text{moles of NaOH} = \text{concentration (mM)} \times \text{volume (L)}moles of NaOH=concentration (mM)×volume (L) For 50 mL (0.050 L): moles of NaOH=20 mM×0.050 L=1 mmol\text{moles of NaOH} = 20 \, \text{mM} \times 0.050 \, \text{L} = 1 \, \text{mmol}moles of NaOH=20mM×0.050L=1mmol
Step 3: Convert moles of NaOH to mass
- To find the mass of NaOH, we use the molar mass of NaOH, which is 40 g/mol.
- Mass (g) = moles × molar mass mass of NaOH=1 mmol×40 g1000 mmol=0.04 g=40 mg\text{mass of NaOH} = 1 \, \text{mmol} \times \frac{40 \, \text{g}}{1000 \, \text{mmol}} = 0.04 \, \text{g} = 40 \, \text{mg}mass of NaOH=1mmol×1000mmol40g=0.04g=40mg
Step 4: Conclusion
- To prepare 50 mL of a 20 mM NaOH solution, you need 40 mg of NaOH.
Therefore, the correct answer is d. Mix 40mg of NaOH and fill with water up to 50mL.
Explanation of other options:
- a. Mix 40g of NaOH and fill with water up to 50mL: This is too much NaOH. 40 grams would make a much higher concentration.
- b. Mix 80mg of NaOH and fill with water up to 50mL: This is too much. You need only 40mg.
- c. Mix 80g of NaOH and fill with water up to 50mL: Again, this is far too much for 50 mL. 80 grams would result in a highly concentrated solution.
Therefore, d is the right choice.
