What is the molarity of `H_(2)SO_(4)` solution that has a density 1.84 g/c c at `35^(@)`C and contains 98% by weight?

Options

A. `4.18M`
B. `8.14M`
C. `18.4M`
D. `18M`

Explanation

To find the molarity of the `H₂SO₄` solution, we will follow these steps:

### Step 1: Understand the definition of molarity
Molarity (M) is defined as the number of moles of solute per liter of solution. The formula for molarity can be expressed as:
\[ \text{Molarity (M)} = \frac{n}{V} \]
where \( n \) is the number of moles of solute and \( V \) is the volume of the solution in liters.

### Step 2: Calculate the mass of the solution
Given that the density of the solution is 1.84 g/cm³ and it contains 98% by weight of `H₂SO₄`, we can assume a convenient mass of the solution. Let's take 100 g of the solution for simplicity.

### Step 3: Calculate the mass of `H₂SO₄`
Since the solution is 98% by weight `H₂SO₄`, the mass of `H₂SO₄` in 100 g of solution is:
\[ \text{Mass of } H₂SO₄ = 0.98 \times 100 \text{ g} = 98 \text{ g} \]

### Step 4: Calculate the number of moles of `H₂SO₄`
To find the number of moles, we need the molar mass of `H₂SO₄`. The molar mass of `H₂SO₄` is:
\[ \text{Molar mass of } H₂SO₄ = 2(1) + 32 + 4(16) = 98 \text{ g/mol} \]
Now, we can calculate the number of moles:
\[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{98 \text{ g}}{98 \text{ g/mol}} = 1 \text{ mol} \]

### Step 5: Calculate the volume of the solution
To find the volume of the solution, we can use the density:
\[ \text{Density} = \frac{\text{mass}}{\text{volume}} \]
Rearranging gives us:
\[ \text{Volume} = \frac{\text{mass}}{\text{density}} = \frac{100 \text{ g}}{1.84 \text{ g/cm}^3} \]
Calculating this gives:
\[ \text{Volume} = 54.34 \text{ cm}^3 = 0.05434 \text{ L} \]

### Step 6: Calculate the molarity
Now we can substitute the values into the molarity formula:
\[ M = \frac{n}{V} = \frac{1 \text{ mol}}{0.05434 \text{ L}} \]
Calculating this gives:
\[ M \approx 18.4 \text{ mol/L} \]

### Final Answer
The molarity of the `H₂SO₄` solution is approximately **18.4 M**.

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