Calculate the pH of the following solutions
Solution of `H_2SO_4` containing 0.98 g of `H_2SO_4` per litre.

Answer

To calculate the pH of a solution of \( H_2SO_4 \) containing 0.98 g of \( H_2SO_4 \) per liter, we can follow these steps:

### Step 1: Calculate the number of moles of \( H_2SO_4 \)

First, we need to find the number of moles of \( H_2SO_4 \) in the solution. The formula to calculate moles is:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

The molar mass of \( H_2SO_4 \) (sulfuric acid) is approximately 98 g/mol. Given that we have 0.98 g of \( H_2SO_4 \):

\[ \text{Number of moles} = \frac{0.98 \, \text{g}}{98 \, \text{g/mol}} = 0.01 \, \text{moles} \]

### Step 2: Calculate the molarity of the solution

Molarity (M) is defined as the number of moles of solute per liter of solution. Since the volume of the solution is 1 liter:

\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume (L)}} = \frac{0.01 \, \text{moles}}{1 \, \text{L}} = 0.01 \, \text{M} \]

### Step 3: Determine the concentration of hydrogen ions

Sulfuric acid (\( H_2SO_4 \)) is a strong acid and dissociates completely in solution to produce two hydrogen ions (\( H^+ \)) for each molecule of \( H_2SO_4 \):

\[ H_2SO_4 \rightarrow 2H^+ + SO_4^{2-} \]

Thus, the concentration of hydrogen ions will be twice the molarity of \( H_2SO_4 \):

\[ \text{Concentration of } H^+ = 2 \times 0.01 \, \text{M} = 0.02 \, \text{M} \]

### Step 4: Calculate the pH of the solution

The pH is calculated using the formula:

\[ \text{pH} = -\log[H^+] \]

Substituting the concentration of hydrogen ions:

\[ \text{pH} = -\log(0.02) \]

To simplify this calculation, we can express 0.02 in scientific notation:

\[ 0.02 = 2 \times 10^{-2} \]

Using the logarithmic properties:

\[ \text{pH} = -\log(2 \times 10^{-2}) = -\log(2) - \log(10^{-2}) = -\log(2) + 2 \]

Using the approximate value \( \log(2) \approx 0.301 \):

\[ \text{pH} = -0.301 + 2 = 1.699 \]

Thus, rounding to one decimal place, we find:

\[ \text{pH} \approx 1.7 \]

### Final Answer:
The pH of the \( H_2SO_4 \) solution is approximately **1.7**.

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