How many grams of NaOH should be added to water to prepare 250 ml solution of 2 M NaOH?

Options

A. `9.6 xx 10^(3)`
B. `2.4 xx 10^(3)`
C. 20
D. 24

Answer

To determine how many grams of NaOH should be added to prepare a 250 ml solution of 2 M NaOH, we can follow these steps:

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

### Step 2: Calculate the number of moles needed
We need to find the number of moles of NaOH required for a 2 M solution in 250 ml. First, convert 250 ml to liters:
\[ 250 \text{ ml} = 0.250 \text{ L} \]

Now, using the molarity formula:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume in liters} \]
\[ \text{Number of moles} = 2 \text{ M} \times 0.250 \text{ L} = 0.5 \text{ moles} \]

### Step 3: Calculate the mass of NaOH required
Next, we need to calculate the mass of NaOH required using the number of moles and the molar mass of NaOH. The molar mass of NaOH can be calculated as follows:
- Sodium (Na) = 23 g/mol
- Oxygen (O) = 16 g/mol
- Hydrogen (H) = 1 g/mol

Thus, the molar mass of NaOH is:
\[ \text{Molar mass of NaOH} = 23 + 16 + 1 = 40 \text{ g/mol} \]

Now, we can calculate the mass of NaOH required:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]
\[ \text{Mass} = 0.5 \text{ moles} \times 40 \text{ g/mol} = 20 \text{ g} \]

### Step 4: Conclusion
To prepare a 250 ml solution of 2 M NaOH, you need to add **20 grams of NaOH** to water.

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