`100mL` of `H_(2)SO_(4)` solution having molarity `1M` and density `1.5g//mL` is mixed with `400mL` of water. Calculate final molarity of `H_(2)SO_(4)` solution, if final density is `1.25g//mL`?

Options

A. `4.4 M`
B. `0.145 M`
C. `0.52 M`
D. `0.227 M`

Answer

To solve the problem step by step, we will follow the calculations as outlined in the video transcript.

### Step 1: Calculate the mass of the H₂SO₄ solution
We know the density and volume of the H₂SO₄ solution. The formula for mass is:

\[ \text{Mass} = \text{Density} \times \text{Volume} \]

Given:
- Density of H₂SO₄ solution = 1.5 g/mL
- Volume of H₂SO₄ solution = 100 mL

Calculating the mass:

\[ \text{Mass of H₂SO₄ solution} = 1.5 \, \text{g/mL} \times 100 \, \text{mL} = 150 \, \text{g} \]

### Step 2: Calculate the mass of water
Next, we calculate the mass of water using its density and volume.

Given:
- Density of water = 1 g/mL
- Volume of water = 400 mL

Calculating the mass:

\[ \text{Mass of water} = 1 \, \text{g/mL} \times 400 \, \text{mL} = 400 \, \text{g} \]

### Step 3: Calculate the total mass of the solution
Now, we can find the total mass of the solution by adding the mass of the H₂SO₄ solution and the mass of water.

\[ \text{Total mass of solution} = \text{Mass of H₂SO₄} + \text{Mass of water} = 150 \, \text{g} + 400 \, \text{g} = 550 \, \text{g} \]

### Step 4: Calculate the volume of the final solution
Using the total mass of the solution and the final density, we can calculate the volume of the final solution.

Given:
- Final density of solution = 1.25 g/mL

Using the formula for volume:

\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

Calculating the volume:

\[ \text{Volume of final solution} = \frac{550 \, \text{g}}{1.25 \, \text{g/mL}} = 440 \, \text{mL} \]

Converting this to liters:

\[ \text{Volume in liters} = \frac{440 \, \text{mL}}{1000} = 0.44 \, \text{L} \]

### Step 5: Calculate the number of moles of H₂SO₄
We know the initial molarity and volume of the H₂SO₄ solution, so we can calculate the number of moles.

Given:
- Molarity (M) = 1 M
- Volume of H₂SO₄ solution = 100 mL = 0.1 L

Using the formula for moles:

\[ \text{Moles} = \text{Molarity} \times \text{Volume} \]

Calculating the number of moles:

\[ \text{Moles of H₂SO₄} = 1 \, \text{mol/L} \times 0.1 \, \text{L} = 0.1 \, \text{moles} \]

### Step 6: Calculate the final molarity of the H₂SO₄ solution
Finally, we can calculate the final molarity of the H₂SO₄ solution using the number of moles and the final volume.

Using the formula for molarity:

\[ \text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \]

Calculating the final molarity:

\[ \text{Final molarity} = \frac{0.1 \, \text{moles}}{0.44 \, \text{L}} \approx 0.227 \, \text{M} \]

### Final Answer
The final molarity of the H₂SO₄ solution is approximately **0.227 M**.

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