Which of the following should be done in order to prepare 0.40 M NaCI starting with 100 ml of 0.30 M NaCI (Mol. Mass of NaCI = 58.5)?

Options

A. Add 0.585 g NaCI
B. Add 20 ml water
C. Add 0.010 ml NaCI
D. Evaporate 10 ml water

Answer

To prepare a 0.40 M NaCl solution starting with 100 mL of a 0.30 M NaCl solution, follow these steps:

### Step 1: Calculate the number of moles of NaCl in the initial solution
We know that molarity (M) is defined as the number of moles of solute per liter of solution.

Given:
- Molarity of initial solution (M1) = 0.30 M
- Volume of initial solution (V1) = 100 mL = 0.100 L

Using the formula:
\[ \text{Number of moles (n)} = M \times V \]
\[ n_1 = 0.30 \, \text{mol/L} \times 0.100 \, \text{L} = 0.030 \, \text{moles} \]

### Step 2: Calculate the number of moles required for the final solution
Now, we need to find the number of moles required for a 0.40 M solution.

Given:
- Molarity of final solution (M2) = 0.40 M
- Volume of final solution (V2) = 100 mL = 0.100 L

Using the same formula:
\[ n_2 = 0.40 \, \text{mol/L} \times 0.100 \, \text{L} = 0.040 \, \text{moles} \]

### Step 3: Determine the additional moles of NaCl needed
To find out how many additional moles of NaCl are needed, subtract the moles already present from the moles required:

\[ \text{Additional moles needed} = n_2 - n_1 = 0.040 \, \text{moles} - 0.030 \, \text{moles} = 0.010 \, \text{moles} \]

### Step 4: Convert moles to grams
Now, we need to convert the additional moles of NaCl to grams using the molar mass of NaCl.

Given:
- Molar mass of NaCl = 58.5 g/mol

Using the formula:
\[ \text{Mass (g)} = \text{moles} \times \text{molar mass} \]
\[ \text{Mass of NaCl to add} = 0.010 \, \text{moles} \times 58.5 \, \text{g/mol} = 0.585 \, \text{g} \]

### Conclusion
To prepare 100 mL of a 0.40 M NaCl solution starting with 100 mL of a 0.30 M NaCl solution, you need to add **0.585 g of NaCl**.

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