What is the molarity of a solution containing 10 g of NaOH in 500 mL of solution ?

Options

A. `"0.25 mol L"^(-1)`
B. `"0.75 mol L"^(-1)`
C. `"0.5 mol L"^(-1)`
D. `"1.25 mol L"^(-1)`

Explanation

To find the molarity of a solution containing 10 g of NaOH in 500 mL of solution, we can follow these steps:

### Step 1: Calculate the molar mass of NaOH
- Sodium (Na) has a molar mass of 23 g/mol.
- Oxygen (O) has a molar mass of 16 g/mol.
- Hydrogen (H) has a molar mass of 1 g/mol.

**Molar mass of NaOH = 23 + 16 + 1 = 40 g/mol**

### Step 2: Calculate the number of moles of NaOH
- Use the formula:
\[ \text{Number of moles} = \frac{\text{mass of solute (g)}}{\text{molar mass of solute (g/mol)}} \]
- Here, the mass of NaOH is 10 g and the molar mass is 40 g/mol.

\[ \text{Number of moles} = \frac{10 \text{ g}}{40 \text{ g/mol}} = 0.25 \text{ moles} \]

### Step 3: Convert the volume of the solution from mL to L
- The volume of the solution is given as 500 mL. To convert this to liters:
\[ \text{Volume in L} = \frac{500 \text{ mL}}{1000} = 0.5 \text{ L} \]

### Step 4: Calculate the molarity of the solution
- Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in L}} \]
- Substituting the values we calculated:
\[ \text{Molarity} = \frac{0.25 \text{ moles}}{0.5 \text{ L}} = 0.5 \text{ M} \]

### Final Answer
The molarity of the solution is **0.5 M**.

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