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 number of moles of NaOH
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass of solute (g)}}{\text{molar mass of solute (g/mol)}} \]
The molar mass of NaOH (Sodium Hydroxide) is calculated as follows:
- Sodium (Na) = 23 g/mol
- Oxygen (O) = 16 g/mol
- Hydrogen (H) = 1 g/mol

Thus, the molar mass of NaOH = 23 + 16 + 1 = 40 g/mol.

Now, substituting the values:
\[ \text{Number of moles of NaOH} = \frac{10 \text{ g}}{40 \text{ g/mol}} = 0.25 \text{ moles} \]

### Step 2: 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:
\[ \text{Volume in liters} = \frac{500 \text{ mL}}{1000} = 0.5 \text{ L} \]

### Step 3: Calculate the molarity of the solution
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]
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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