The molarity of 98% by wt. `H_(2)SO_(4)` (d = 1.8 g/ml) is

Options

A. 6 M
B. 18 M
C. 10 M
D. 4 M

Answer

To find the molarity of 98% by weight H₂SO₄ with a density of 1.8 g/mL, we can follow these steps:

### Step 1: Determine the mass of the solute and the mass of the solution
Given that the solution is 98% by weight, this means:
- Mass of H₂SO₄ (solute) = 98 g
- Mass of the solution = 100 g

### Step 2: Calculate the number of moles of H₂SO₄
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass of solute}}{\text{molar mass of solute}} \]

The molar mass of H₂SO₄ is approximately 98 g/mol. Therefore:
\[ \text{Number of moles} = \frac{98 \text{ g}}{98 \text{ g/mol}} = 1 \text{ mole} \]

### Step 3: Calculate the volume of the solution
Using the density formula:
\[ \text{Density} = \frac{\text{mass}}{\text{volume}} \]
We can rearrange this to find the volume:
\[ \text{Volume} = \frac{\text{mass of solution}}{\text{density}} \]

Substituting the values:
\[ \text{Volume} = \frac{100 \text{ g}}{1.8 \text{ g/mL}} \approx 55.56 \text{ mL} \]

### Step 4: Convert the volume from mL to L
Since molarity is expressed in moles per liter, we need to convert the volume from mL to L:
\[ 55.56 \text{ mL} = \frac{55.56}{1000} \text{ L} = 0.05556 \text{ L} \]

### Step 5: Calculate the molarity
Molarity (M) is defined as:
\[ M = \frac{\text{number of moles of solute}}{\text{volume of solution in liters}} \]

Substituting the values we found:
\[ M = \frac{1 \text{ mole}}{0.05556 \text{ L}} \approx 18 \text{ M} \]

### Final Answer
The molarity of the 98% by weight H₂SO₄ solution is approximately **18 M**.

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