To find the concentration of \( K^+ \) ions in the resulting solution after mixing 250 ml of 0.10 M \( K_2SO_4 \) with 250 ml of 0.20 M \( KCl \), we can follow these steps:
### Step 1: Calculate the moles of \( K_2SO_4 \)
The molarity (M) of a solution is defined as the number of moles of solute divided by the volume of solution in liters.
Given:
- Volume of \( K_2SO_4 \) solution = 250 ml = 0.250 L
- Molarity of \( K_2SO_4 \) = 0.10 M
Using the formula:
\[
\text{Moles of } K_2SO_4 = \text{Molarity} \times \text{Volume} = 0.10 \, \text{mol/L} \times 0.250 \, \text{L} = 0.025 \, \text{moles}
\]
### Step 2: Calculate the moles of \( K^+ \) from \( K_2SO_4 \)
Each molecule of \( K_2SO_4 \) produces 2 \( K^+ \) ions. Therefore, the moles of \( K^+ \) ions from \( K_2SO_4 \) is:
\[
\text{Moles of } K^+ \text{ from } K_2SO_4 = 2 \times \text{Moles of } K_2SO_4 = 2 \times 0.025 = 0.050 \, \text{moles}
\]
### Step 3: Calculate the moles of \( KCl \)
Given:
- Volume of \( KCl \) solution = 250 ml = 0.250 L
- Molarity of \( KCl \) = 0.20 M
Using the formula:
\[
\text{Moles of } KCl = \text{Molarity} \times \text{Volume} = 0.20 \, \text{mol/L} \times 0.250 \, \text{L} = 0.050 \, \text{moles}
\]
### Step 4: Calculate the moles of \( K^+ \) from \( KCl \)
Each molecule of \( KCl \) produces 1 \( K^+ \) ion. Therefore, the moles of \( K^+ \) ions from \( KCl \) is:
\[
\text{Moles of } K^+ \text{ from } KCl = \text{Moles of } KCl = 0.050 \, \text{moles}
\]
### Step 5: Calculate the total moles of \( K^+ \)
Now, we can find the total moles of \( K^+ \) ions in the resulting solution:
\[
\text{Total moles of } K^+ = \text{Moles of } K^+ \text{ from } K_2SO_4 + \text{Moles of } K^+ \text{ from } KCl = 0.050 + 0.050 = 0.100 \, \text{moles}
\]
### Step 6: Calculate the total volume of the resulting solution
The total volume after mixing the two solutions is:
\[
\text{Total volume} = 250 \, \text{ml} + 250 \, \text{ml} = 500 \, \text{ml} = 0.500 \, \text{L}
\]
### Step 7: Calculate the concentration of \( K^+ \) ions
Finally, we can calculate the concentration of \( K^+ \) ions in the resulting solution:
\[
\text{Concentration of } K^+ = \frac{\text{Total moles of } K^+}{\text{Total volume in L}} = \frac{0.100 \, \text{moles}}{0.500 \, \text{L}} = 0.200 \, \text{M}
\]
### Final Answer
The concentration of \( K^+ \) ions in the resulting solution is **0.200 M**.
