300 gm, `30%`(w/w) NaOH solution is mixed with 500 gm `40%`(w/w) NaOH solution. What is `%` (w/v) NaOH if density of final solution is 2 gm/mL?

Options

A. 72.5
B. 65
C. 62.5
D. None

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the mass of NaOH in each solution.

1. **For the 300 gm solution (30% w/w):**
\[ \text{Mass of NaOH} = 300 \, \text{gm} \times \frac{30}{100} = 90 \, \text{gm} \]

2. **For the 500 gm solution (40% w/w):**
\[ \text{Mass of NaOH} = 500 \, \text{gm} \times \frac{40}{100} = 200 \, \text{gm} \]

### Step 2: Calculate the total mass of NaOH.

\[ \text{Total mass of NaOH} = 90 \, \text{gm} + 200 \, \text{gm} = 290 \, \text{gm} \]

### Step 3: Calculate the total mass of the final solution.

\[ \text{Total mass of solution} = 300 \, \text{gm} + 500 \, \text{gm} = 800 \, \text{gm} \]

### Step 4: Calculate the volume of the final solution using density.

Given that the density of the final solution is 2 gm/mL, we can find the volume of the solution:

\[ \text{Volume of solution} = \frac{\text{Total mass of solution}}{\text{Density}} = \frac{800 \, \text{gm}}{2 \, \text{gm/mL}} = 400 \, \text{mL} \]

### Step 5: Calculate the % (w/v) of NaOH in the final solution.

The % (w/v) is calculated using the formula:

\[ \text{Percentage (w/v)} = \left( \frac{\text{Mass of solute (NaOH)}}{\text{Volume of solution (mL)}} \right) \times 100 \]

Substituting the values we found:

\[ \text{Percentage (w/v)} = \left( \frac{290 \, \text{gm}}{400 \, \text{mL}} \right) \times 100 = 72.5\% \]

### Final Answer:
The % (w/v) of NaOH in the final solution is **72.5%**.

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