`150 cm^3` of a decimolar NaOH solution is diluted to `750 cm^3`. Find the molarity of the diluted solution.

Answer

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

### Step 1: Understand the Initial Conditions
We have an initial solution of NaOH with a concentration of 0.1 M (decimolar) and a volume of 150 cm³ (or 0.150 L).

### Step 2: Convert the Initial Molarity
The initial molarity (M1) is given as decimolar, which can be expressed as:
\[ M1 = 0.1 \, \text{M} \]

### Step 3: Identify the Final Volume
The final volume (V2) after dilution is given as 750 cm³, which can be converted to liters:
\[ V2 = 750 \, \text{cm}^3 = 0.750 \, \text{L} \]

### Step 4: Use the Dilution Formula
The dilution formula relates the initial and final molarity and volume:
\[ M1 \times V1 = M2 \times V2 \]
Where:
- \( M1 \) = initial molarity
- \( V1 \) = initial volume
- \( M2 \) = final molarity (what we want to find)
- \( V2 \) = final volume

### Step 5: Rearrange the Formula to Solve for M2
We can rearrange the formula to solve for \( M2 \):
\[ M2 = \frac{M1 \times V1}{V2} \]

### Step 6: Substitute the Known Values
Now, substitute the known values into the equation:
\[ M2 = \frac{0.1 \, \text{M} \times 0.150 \, \text{L}}{0.750 \, \text{L}} \]

### Step 7: Calculate M2
Now, perform the calculation:
\[ M2 = \frac{0.015 \, \text{mol}}{0.750 \, \text{L}} \]
\[ M2 = 0.02 \, \text{M} \]

### Step 8: Convert to Millimolar
To express this in millimolar (mM), we multiply by 1000:
\[ M2 = 0.02 \, \text{M} = 20 \, \text{mM} \]

### Final Answer
The molarity of the diluted NaOH solution is **20 mM**.

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