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: Identify the initial conditions
- Initial volume of the solution (V1) = 500 ml
- Initial molarity of the solution (M1) = 0.2 M
- Volume of water added = 200 ml

### Step 2: Calculate the total volume after dilution
- Total volume after adding water (V2) = Initial volume + Volume of water added
- V2 = 500 ml + 200 ml = 700 ml

### Step 3: Use the dilution formula
The dilution formula is given by:
\[ M1 \times V1 = M2 \times V2 \]
Where:
- M1 = initial molarity
- V1 = initial volume
- M2 = final molarity (what we need to find)
- V2 = final volume

### Step 4: Substitute the known values into the formula
- Substitute M1 = 0.2 M, V1 = 500 ml, and V2 = 700 ml into the equation:
\[ 0.2 \, \text{M} \times 500 \, \text{ml} = M2 \times 700 \, \text{ml} \]

### Step 5: Solve for M2
- Rearranging the equation to solve for M2:
\[ M2 = \frac{0.2 \, \text{M} \times 500 \, \text{ml}}{700 \, \text{ml}} \]
- Calculate the numerator:
\[ 0.2 \times 500 = 100 \]
- Now substitute back:
\[ M2 = \frac{100}{700} \]

### Step 6: Simplify the fraction
- Simplifying \( \frac{100}{700} \):
\[ M2 = \frac{1}{7} \, \text{M} \]
- Converting to decimal:
\[ M2 \approx 0.1428 \, \text{M} \]

### Final Answer
The molarity of the diluted solution is approximately **0.1428 M**.