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 water 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 divided by the volume of solution in liters.

### Step 2: Convert the volume of the solution from ml to liters
Since the volume of the solution is given in milliliters (ml), we need to convert it to liters (L):
\[ 250 \, \text{ml} = \frac{250}{1000} \, \text{L} = 0.250 \, \text{L} \]

### Step 3: Use the molarity formula to find the number of moles of NaOH
Using the molarity formula:
\[ \text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
We can rearrange this to find the number of moles of NaOH:
\[ \text{moles of NaOH} = \text{Molarity} \times \text{Volume in L} \]
Substituting the values:
\[ \text{moles of NaOH} = 2 \, \text{M} \times 0.250 \, \text{L} = 0.500 \, \text{moles} \]

### Step 4: Calculate the mass of NaOH needed
To find the mass of NaOH, we use the formula:
\[ \text{mass} = \text{moles} \times \text{molar mass} \]
The molar mass of NaOH (sodium hydroxide) is approximately 40 g/mol. Therefore:
\[ \text{mass of NaOH} = 0.500 \, \text{moles} \times 40 \, \text{g/mol} = 20 \, \text{grams} \]

### 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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