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 that the mass of NaOH is 1 mg, we convert it to grams:
\[ \text{Mass of NaOH} = 1 \, \text{mg} = 1 \times 10^{-3} \, \text{g} \]

### Step 2: Calculate the number of moles of NaOH.
The molar mass of NaOH is 40 g/mol. We can calculate the number of moles using the formula:
\[ \text{Number of moles} = \frac{\text{Mass (g)}}{\text{Molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{1 \times 10^{-3} \, \text{g}}{40 \, \text{g/mol}} = \frac{1}{40} \times 10^{-3} \, \text{mol} \]

### Step 3: Convert the volume of the solution from milliliters to liters.
Given that the volume of the solution is 250 mL, we convert it to liters:
\[ \text{Volume of solution} = 250 \, \text{mL} = 250 \times 10^{-3} \, \text{L} = 0.250 \, \text{L} \]

### Step 4: Calculate the molarity of the NaOH solution.
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{Number of moles of solute}}{\text{Volume of solution (L)}} \]
Substituting the values we calculated:
\[ \text{Molarity} = \frac{\frac{1 \times 10^{-3}}{40}}{0.250} \]
This simplifies to:
\[ \text{Molarity} = \frac{1 \times 10^{-3}}{40 \times 0.250} = \frac{1 \times 10^{-3}}{10} = 1 \times 10^{-4} \, \text{M} \]

### Final Answer:
The molarity of the NaOH solution is:
\[ \text{Molarity} = 1 \times 10^{-4} \, \text{M} \]