To solve the problem of calculating the volume of \(0.2 \, M \, H_2SO_4\) required to produce \(3.4 \, g \, H_2S\), we will follow these steps:
### Step 1: Write the balanced chemical equation
The reaction between \(H_2SO_4\) and \(KI\) produces \(I_2\) and \(H_2S\). The balanced equation is:
\[
5H_2SO_4 + 8KI \rightarrow 4I_2 + H_2S + 4H_2O
\]
### Step 2: Calculate the molar mass of \(H_2S\)
The molar mass of \(H_2S\) is calculated as follows:
- Hydrogen (H): \(1.01 \, g/mol\) (2 atoms)
- Sulfur (S): \(32.07 \, g/mol\) (1 atom)
\[
\text{Molar mass of } H_2S = (2 \times 1.01) + 32.07 = 34.09 \, g/mol
\]
### Step 3: Calculate the number of moles of \(H_2S\)
Using the mass of \(H_2S\) given:
\[
\text{Number of moles of } H_2S = \frac{\text{mass}}{\text{molar mass}} = \frac{3.4 \, g}{34.09 \, g/mol} \approx 0.0997 \, mol
\]
### Step 4: Use stoichiometry to find moles of \(H_2SO_4\)
From the balanced equation, we see that 5 moles of \(H_2SO_4\) produce 1 mole of \(H_2S\):
\[
\text{Moles of } H_2SO_4 = 0.0997 \, mol \times \frac{5 \, mol \, H_2SO_4}{1 \, mol \, H_2S} \approx 0.4985 \, mol
\]
### Step 5: Calculate the volume of \(H_2SO_4\) solution needed
Using the molarity equation:
\[
\text{Molarity (M)} = \frac{\text{moles}}{\text{volume (L)}}
\]
Rearranging gives:
\[
\text{Volume (L)} = \frac{\text{moles}}{\text{Molarity}} = \frac{0.4985 \, mol}{0.2 \, mol/L} = 2.4925 \, L
\]
### Step 6: Convert volume from liters to milliliters
\[
\text{Volume (mL)} = 2.4925 \, L \times 1000 \, mL/L = 2492.5 \, mL
\]
### Step 7: Final calculation and rounding
Since we need the volume of \(0.2 \, M \, H_2SO_4\) to produce \(3.4 \, g \, H_2S\), the final answer is approximately:
\[
\text{Volume} \approx 2492.5 \, mL
\]
### Summary of the Steps:
1. Write the balanced chemical equation.
2. Calculate the molar mass of \(H_2S\).
3. Calculate the number of moles of \(H_2S\) from the given mass.
4. Use stoichiometry to find the moles of \(H_2SO_4\) needed.
5. Calculate the volume of \(H_2SO_4\) solution required.
6. Convert the volume to milliliters.
