Concentrated sulphuric acid has density of 1.9 g/mL and 99% `H_(2)SO_(4)` by mass. Calculate the molarity of the acid.

Answer

To calculate the molarity of concentrated sulfuric acid, we will follow these steps:

### Step 1: Understand the Given Information
- Density of concentrated sulfuric acid = 1.9 g/mL
- Mass percentage of H₂SO₄ = 99%
- We will assume we have 100 g of the solution for easier calculations.

### Step 2: Calculate the Mass of H₂SO₄
Since the solution is 99% H₂SO₄ by mass:
\[ \text{Mass of H₂SO₄} = 99\% \text{ of 100 g} = 99 \text{ g} \]

### 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:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{100 \text{ g}}{1.9 \text{ g/mL}} \approx 52.63 \text{ mL} \]
Now, convert this volume from mL to L:
\[ \text{Volume in L} = \frac{52.63 \text{ mL}}{1000} \approx 0.05263 \text{ L} \]

### Step 4: Calculate the Number of Moles of H₂SO₄
To find the number of moles, we use the molar mass of H₂SO₄:
\[ \text{Molar mass of H₂SO₄} = 2(1) + 32 + 4(16) = 98 \text{ g/mol} \]
Now, calculate the number of moles:
\[ \text{Number of moles of H₂SO₄} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{99 \text{ g}}{98 \text{ g/mol}} \approx 1.01 \text{ mol} \]

### Step 5: Calculate the Molarity
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in L}} = \frac{1.01 \text{ mol}}{0.05263 \text{ L}} \approx 19.19 \text{ M} \]

### Final Answer
The molarity of the concentrated sulfuric acid is approximately **19.19 M**.

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