The `P^(H)` of a sample of `H_(2)SO_(4)` is `1.3979`. The percentage of the solution is `73.5% (w//w)`, the density of the solution is

Options

A. `2.66 xx 10^(-3) g//c c`
B. `5.32 xx 10^(-3) g// c c`
C. `1.33 xx 10^(-3) g// c c`
D. `0.01 g//c c`

Explanation

To find the density of the `H₂SO₄` solution given the pH, percentage concentration, and the equivalent weight, we can follow these steps:

### Step 1: Calculate the concentration of H⁺ ions from pH
The pH of the solution is given as `1.3979`. We can calculate the concentration of H⁺ ions using the formula:
\[ \text{pH} = -\log[H^+] \]
To find [H⁺], we take the antilog:
\[ [H^+] = 10^{-\text{pH}} \]
Substituting the value of pH:
\[ [H^+] = 10^{-1.3979} \approx 4.0 \times 10^{-2} \, \text{mol/L} \]

### Step 2: Determine the normality of the `H₂SO₄` solution
For sulfuric acid, `H₂SO₄`, each molecule can release 2 H⁺ ions. Therefore, the normality (N) is twice the molarity (M):
\[ N = 2 \times [H^+] = 2 \times 4.0 \times 10^{-2} \approx 8.0 \times 10^{-2} \, \text{N} \]

### Step 3: Use the weight/weight percentage to find the density
The weight/weight percentage of `H₂SO₄` is given as `73.5% (w/w)`. This means that in 100 grams of solution, there are 73.5 grams of `H₂SO₄`.

### Step 4: Calculate the equivalent weight of `H₂SO₄`
The molecular weight of `H₂SO₄` is approximately 98 g/mol. The equivalent weight (EW) can be calculated as:
\[ \text{EW} = \frac{\text{Molecular Weight}}{\text{n}} \]
where n is the number of H⁺ ions released per molecule, which is 2 for `H₂SO₄`:
\[ \text{EW} = \frac{98}{2} = 49 \, \text{g/equiv} \]

### Step 5: Calculate the density using the normality and equivalent weight
The formula for density (d) in terms of normality (N), weight percentage (w/w), and equivalent weight (EW) is:
\[ d = \frac{N \times EW}{\text{weight percentage}} \times 10 \]
Substituting the values we have:
\[ d = \frac{8.0 \times 10^{-2} \times 49}{73.5} \times 10 \]
Calculating this gives:
\[ d \approx \frac{3.92}{73.5} \times 10 \approx 0.533 \, \text{g/cm}^3 \]

### Final Result
Thus, the density of the `H₂SO₄` solution is approximately **0.533 g/cm³**.

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