200 ml of water is added of 500 ml of 0.2 M solution. What is the molarity of this diluted solution?

Options

A. 0.7093 M
B. 0.1428 M
C. 0.4005 M
D. 0.2897 M

Answer

To find the molarity of the diluted solution after adding 200 ml of water to 500 ml of a 0.2 M solution, we can follow these steps:

### Step 1: Calculate the moles of solute in the original solution
The formula for molarity (M) is:
\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
Given:
- Molarity (M) = 0.2 M
- Volume of solution = 500 ml = 0.5 L (since 1000 ml = 1 L)

Now, we can calculate the moles of solute:
\[ \text{moles of solute} = M \times \text{volume in liters} = 0.2 \, \text{mol/L} \times 0.5 \, \text{L} = 0.1 \, \text{moles} \]

### Step 2: Determine the total volume of the diluted solution
When we add 200 ml of water to the original 500 ml solution, the total volume becomes:
\[ \text{Total volume} = 500 \, \text{ml} + 200 \, \text{ml} = 700 \, \text{ml} = 0.7 \, \text{L} \]

### Step 3: Calculate the molarity of the diluted solution
Now, we can find the molarity of the diluted solution using the moles of solute and the new total volume:
\[ \text{Molarity of diluted solution} = \frac{\text{moles of solute}}{\text{total volume in liters}} = \frac{0.1 \, \text{moles}}{0.7 \, \text{L}} \approx 0.142857 \, \text{M} \]

### Step 4: Round the answer
Rounding off to four decimal places, we get:
\[ \text{Molarity of diluted solution} \approx 0.1429 \, \text{M} \]

### Final Answer
The molarity of the diluted solution is approximately **0.1429 M**.

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