500 ml of `2 M CH_(3)COOH` solution is mixid with `600 ml 12 % w//v CH_(3)COOH` solution then calculate the final molarity of solution.

Answer

To solve the problem of finding the final molarity of the solution after mixing 500 ml of 2 M CH₃COOH with 600 ml of a 12% w/v CH₃COOH solution, we can follow these steps:

### Step 1: Calculate the moles of CH₃COOH in the first solution
We know that molarity (M) is defined as moles of solute per liter of solution.

For the first solution:
- Molarity (M₁) = 2 M
- Volume (V₁) = 500 ml = 0.5 L

Using the formula:
\[ \text{Moles} = \text{Molarity} \times \text{Volume} \]
\[ \text{Moles of CH₃COOH in first solution} = 2 \, \text{mol/L} \times 0.5 \, \text{L} = 1 \, \text{mol} \]

### Step 2: Calculate the moles of CH₃COOH in the second solution
For the second solution, we have a 12% w/v solution. This means there are 12 grams of CH₃COOH in 100 ml of solution.

To find the number of moles:
1. Calculate the total grams in 600 ml:
\[ \text{Grams in 600 ml} = 12 \, \text{g/100 ml} \times 600 \, \text{ml} = 72 \, \text{g} \]

2. Convert grams to moles using the molar mass of CH₃COOH (approximately 60 g/mol):
\[ \text{Moles of CH₃COOH in second solution} = \frac{72 \, \text{g}}{60 \, \text{g/mol}} = 1.2 \, \text{mol} \]

### Step 3: Calculate the total moles of CH₃COOH after mixing
Now, we can add the moles from both solutions:
\[ \text{Total moles} = 1 \, \text{mol} + 1.2 \, \text{mol} = 2.2 \, \text{mol} \]

### Step 4: Calculate the final volume of the mixed solution
The total volume after mixing is:
\[ \text{Total volume} = 500 \, \text{ml} + 600 \, \text{ml} = 1100 \, \text{ml} = 1.1 \, \text{L} \]

### Step 5: Calculate the final molarity of the solution
Using the total moles and total volume, we can find the final molarity (M_final):
\[ \text{Molarity} = \frac{\text{Total moles}}{\text{Total volume}} \]
\[ M_{\text{final}} = \frac{2.2 \, \text{mol}}{1.1 \, \text{L}} = 2 \, \text{M} \]

### Final Answer
The final molarity of the solution is **2 M**.

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