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

Options

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

Explanation

To find the molarity of a 98% `H₂SO₄` solution with a density of 1.8 g/ml, we can follow these steps:

### Step 1: Understand the composition of the solution
98% `H₂SO₄` by weight means that in 100 grams of the solution, there are 98 grams of sulfuric acid (`H₂SO₄`).

### Step 2: Calculate the number of moles of `H₂SO₄`
To find the number of moles, we use the formula:
\[ \text{Number of moles (n)} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
The molar mass of `H₂SO₄` is approximately 98 g/mol. Therefore:
\[ n = \frac{98 \text{ g}}{98 \text{ g/mol}} = 1 \text{ mole} \]

### Step 3: Calculate the volume of the solution
Using the density to find the volume of the solution:
\[ \text{Density} = \frac{\text{mass}}{\text{volume}} \implies \text{volume} = \frac{\text{mass}}{\text{density}} \]
Here, the mass of the solution is 100 grams and the density is 1.8 g/ml:
\[ \text{Volume} = \frac{100 \text{ g}}{1.8 \text{ g/ml}} \approx 55.56 \text{ ml} \]

### Step 4: Convert volume from ml to liters
Since molarity is expressed in moles per liter, we convert the volume from ml to liters:
\[ 55.56 \text{ ml} = 55.56 \times 10^{-3} \text{ L} = 0.05556 \text{ L} \]

### Step 5: Calculate the molarity
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity (M)} = \frac{\text{Number of moles}}{\text{Volume in liters}} = \frac{1 \text{ mole}}{0.05556 \text{ L}} \approx 18 \text{ mol/L} \]

### Final Answer
The molarity of the 98% `H₂SO₄` solution is approximately **18 mol/L**.

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