100 mL of a solution containing 5 g of NaOH are mixed with 200 mL of `(M)/(5)` NaOH solution . Calculate the molartiy of the resulting solutions.

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Calculate the number of moles of NaOH in Solution A
We have 5 g of NaOH in 100 mL of Solution A.

1. **Molar mass of NaOH** = 40 g/mol
2. **Number of moles of NaOH** = mass (g) / molar mass (g/mol)
\[ \text{Moles of NaOH} = \frac{5 \, \text{g}}{40 \, \text{g/mol}} = 0.125 \, \text{mol} \]

### Step 2: Calculate the molarity of Solution A
Molarity (M) is defined as the number of moles of solute per liter of solution.

1. **Volume of Solution A** = 100 mL = 0.1 L
2. **Molarity of Solution A (M_A)** = moles of solute / volume of solution in liters
\[ M_A = \frac{0.125 \, \text{mol}}{0.1 \, \text{L}} = 1.25 \, \text{M} \]

### Step 3: Calculate the number of moles of NaOH in Solution B
We are given that Solution B has a molarity of \( \frac{1}{5} \) M and a volume of 200 mL.

1. **Convert the molarity to decimal**: \( \frac{1}{5} = 0.2 \, \text{M} \)
2. **Volume of Solution B** = 200 mL = 0.2 L
3. **Number of moles of NaOH in Solution B** = Molarity × Volume
\[ \text{Moles of NaOH in B} = 0.2 \, \text{M} \times 0.2 \, \text{L} = 0.04 \, \text{mol} \]

### Step 4: Calculate the total number of moles of NaOH after mixing
Now, we can find the total number of moles of NaOH when both solutions are mixed.

1. **Total moles of NaOH** = Moles from Solution A + Moles from Solution B
\[ \text{Total moles} = 0.125 \, \text{mol} + 0.04 \, \text{mol} = 0.165 \, \text{mol} \]

### Step 5: Calculate the total volume of the mixed solution
The total volume after mixing both solutions is:

1. **Total Volume** = Volume of Solution A + Volume of Solution B
\[ \text{Total Volume} = 100 \, \text{mL} + 200 \, \text{mL} = 300 \, \text{mL} = 0.3 \, \text{L} \]

### Step 6: Calculate the molarity of the resulting solution
Finally, we can calculate the molarity of the resulting solution.

1. **Molarity of the final solution (M_final)** = Total moles of solute / Total volume in liters
\[ M_{\text{final}} = \frac{0.165 \, \text{mol}}{0.3 \, \text{L}} = 0.55 \, \text{M} \]

### Final Answer:
The molarity of the resulting solution is **0.55 M**.

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