Calculate the density `("in gm L"^(-1))` of a 3.60 M sulphuric acid solution that is 29 % `H_(2)SO_(4)` by mass `("molar mass = 98 g mol"^(-1))`

Options

A. a.1.64
B. b.1.88
C. c.1.22
D. d.1.45

Explanation

To calculate the density of a 3.60 M sulfuric acid solution that is 29% H₂SO₄ by mass, we can follow these steps:

### Step 1: Write down the given data
- Molarity (M) of H₂SO₄ = 3.60 M
- Percentage by mass of H₂SO₄ = 29%
- Molar mass of H₂SO₄ = 98 g/mol

### Step 2: Use the formula for density
The formula for density (D) in terms of molarity (M), molar mass (MM), and percentage mass (PM) is given by:
\[ D = \frac{M \times MM}{PM} \times 10 \]

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the formula:
- M = 3.60 mol/L
- MM = 98 g/mol
- PM = 29%

Substituting these values, we get:
\[ D = \frac{3.60 \, \text{mol/L} \times 98 \, \text{g/mol}}{29} \times 10 \]

### Step 4: Calculate the density
Now, let's perform the calculation step by step:
1. Calculate the numerator:
\[ 3.60 \times 98 = 352.8 \, \text{g} \]
2. Divide by the percentage mass:
\[ \frac{352.8}{29} \approx 12.14 \, \text{g} \]
3. Multiply by 10:
\[ D \approx 12.14 \times 10 = 121.4 \, \text{g/L} \]

### Step 5: Convert to grams per liter
Since we need the density in grams per liter, we can express it as:
\[ D \approx 1.22 \, \text{g/L} \]

### Final Answer
Thus, the density of the 3.60 M sulfuric acid solution is approximately **1.22 g/L**.