What is the molarity of NaOH solution if 250 mL of it contains 1 mg of NaOH ?

Options

A. `10^(-1) M`
B. `10^(-2) M`
C. `10^(-4) M`
D. `10^(-3) M`

Answer

To find the molarity of the NaOH solution, we will follow these steps:

### Step 1: Convert the mass of NaOH from milligrams to grams.
Given:
- Mass of NaOH = 1 mg

To convert milligrams to grams:
\[ 1 \text{ mg} = 1 \times 10^{-3} \text{ g} = 0.001 \text{ g} \]

### Step 2: Convert the volume of the solution from milliliters to liters.
Given:
- Volume of the solution = 250 mL

To convert milliliters to liters:
\[ 250 \text{ mL} = 250 \times 10^{-3} \text{ L} = 0.25 \text{ L} \]

### Step 3: Calculate the number of moles of NaOH.
The formula for calculating moles is:
\[ \text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
The molar mass of NaOH is approximately 40 g/mol. Therefore:
\[ \text{Moles of NaOH} = \frac{0.001 \text{ g}}{40 \text{ g/mol}} = 2.5 \times 10^{-5} \text{ moles} \]

### Step 4: Calculate the molarity of the NaOH solution.
The formula for molarity (M) is:
\[ M = \frac{\text{number of moles of solute}}{\text{volume of solution in liters}} \]
Substituting the values we have:
\[ M = \frac{2.5 \times 10^{-5} \text{ moles}}{0.25 \text{ L}} = 1.0 \times 10^{-4} \text{ M} \]

### Final Answer:
The molarity of the NaOH solution is:
\[ 1.0 \times 10^{-4} \text{ M} \]

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