The molarity and molality of an aqueous solution of `H_(2)SO_(4) "as" M_(1) and M_(2)` respectively. If the molecular mass of `H_(2)SO_(4)` is M, density of the solution is

Options

A. `M_(2)(M_(1)+(M)/(1000))g//ml`
B. `M_(2)((1)/(M_(1))+(M)/(1000))g//ml`
C. `M_(1)((1)/(M_(2))+(M)/(1000))g//ml`
D. `M_(2)(M_(2)+(M)/(1000))g//ml`

Answer

To solve the problem, we need to find the density of an aqueous solution of sulfuric acid (H₂SO₄) using the given molarity (M₁) and molality (M₂), along with the molecular mass (M) of H₂SO₄.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Molarity (M₁)**: It is defined as the number of moles of solute per liter of solution.
- **Molality (M₂)**: It is defined as the number of moles of solute per kilogram of solvent.
- **Molecular Mass (M)**: It is the mass of one mole of a substance, given in grams per mole.

2. **Formula for Density**:
The density (d) of the solution can be calculated using the following formula:
\[ d = \frac{M_1}{M_2} + \frac{M}{1000} \]
where:
- \( M_1 \) is the molarity,
- \( M_2 \) is the molality,
- \( M \) is the molecular mass of H₂SO₄.

3. **Substituting Values**:
Substitute the values of molarity (M₁), molality (M₂), and molecular mass (M) into the formula:
\[ d = \frac{M_1}{M_2} + \frac{M}{1000} \]

4. **Final Expression**:
The final expression for the density of the solution is:
\[ d = \frac{M_1}{M_2} + \frac{M}{1000} \text{ g/mL} \]

5. **Conclusion**:
The density of the aqueous solution of sulfuric acid is given by the formula derived above.