4.0 gm of NaOH are contained in one decilitre of solution. Its molarity would be

Options

A. 4 M
B. 2M
C. 1M
D. 1.5 M

Explanation

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

### Step 1: Understand the formula for molarity
Molarity (M) is defined as the number of moles of solute divided by the volume of solution in liters. The formula is given by:
\[ M = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]

### Step 2: Convert the volume from deciliters to liters
The volume of the solution is given as 1 deciliter (dL). We need to convert this to liters:
\[ 1 \text{ dL} = 0.1 \text{ L} \]

### Step 3: Calculate the number of moles of NaOH
To find the number of moles of NaOH, we use the formula:
\[ \text{Number of moles} = \frac{\text{Weight of solute (g)}}{\text{Molecular weight of solute (g/mol)}} \]
The weight of NaOH is given as 4 grams.

Next, we need to calculate the molecular weight of NaOH:
- Sodium (Na) has an atomic mass of approximately 23 g/mol.
- Oxygen (O) has an atomic mass of approximately 16 g/mol.
- Hydrogen (H) has an atomic mass of approximately 1 g/mol.

Thus, the molecular weight of NaOH is:
\[ \text{Molecular weight of NaOH} = 23 + 16 + 1 = 40 \text{ g/mol} \]

Now, we can calculate the number of moles:
\[ \text{Number of moles} = \frac{4 \text{ g}}{40 \text{ g/mol}} = 0.1 \text{ moles} \]

### Step 4: Substitute values into the molarity formula
Now that we have the number of moles and the volume in liters, we can calculate the molarity:
\[ M = \frac{0.1 \text{ moles}}{0.1 \text{ L}} = 1 \text{ M} \]

### Conclusion
The molarity of the NaOH solution is **1 M**.

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