250 ml of 0.10 M `K_2 SO_4` solution is mixed with 250 ml of 0.20 M KCI solution. The concentration of `K^(+)`ions in the resulting solution will be:

Options

A. 0.1 M
B. 0.4 M
C. 0.2 M
D. 0.8 M

Answer

To find the concentration of \( K^+ \) ions in the resulting solution when 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 \( K_2SO_4 \)
Using the formula:
\[ \text{Moles} = \text{Molarity} \times \text{Volume (in L)} \]
First, convert the volume from ml to L:
\[ 250 \, \text{ml} = 0.250 \, \text{L} \]
Now calculate the moles of \( K_2SO_4 \):
\[ \text{Moles of } K_2SO_4 = 0.10 \, \text{M} \times 0.250 \, \text{L} = 0.025 \, \text{moles} \]

### Step 2: Determine the moles of \( K^+ \) from \( K_2SO_4 \)
From the dissociation of \( K_2SO_4 \):
\[ K_2SO_4 \rightarrow 2K^+ + SO_4^{2-} \]
This means 1 mole of \( K_2SO_4 \) produces 2 moles of \( K^+ \). Therefore, the moles of \( K^+ \) from \( K_2SO_4 \) will be:
\[ \text{Moles of } K^+ \text{ from } K_2SO_4 = 2 \times 0.025 = 0.050 \, \text{moles} \]

### Step 3: Calculate the moles of \( KCl \)
Now, calculate the moles of \( KCl \):
\[ \text{Moles of } KCl = 0.20 \, \text{M} \times 0.250 \, \text{L} = 0.050 \, \text{moles} \]

### Step 4: Determine the moles of \( K^+ \) from \( KCl \)
From the dissociation of \( KCl \):
\[ KCl \rightarrow K^+ + Cl^- \]
This means 1 mole of \( KCl \) produces 1 mole of \( K^+ \). Therefore, the moles of \( K^+ \) from \( KCl \) will be:
\[ \text{Moles of } K^+ \text{ from } KCl = 0.050 \, \text{moles} \]

### Step 5: Calculate the total moles of \( K^+ \)
Now, add the moles of \( K^+ \) from both sources:
\[ \text{Total moles of } K^+ = 0.050 + 0.050 = 0.100 \, \text{moles} \]

### Step 6: Calculate the total volume of the solution
The total volume of the solution after mixing is:
\[ \text{Total Volume} = 250 \, \text{ml} + 250 \, \text{ml} = 500 \, \text{ml} = 0.500 \, \text{L} \]

### Step 7: Calculate the concentration of \( K^+ \)
Finally, use the total moles and total volume to find the concentration:
\[ \text{Concentration of } K^+ = \frac{\text{Total moles of } K^+}{\text{Total Volume (in L)}} = \frac{0.100 \, \text{moles}}{0.500 \, \text{L}} = 0.200 \, \text{M} \]

### Final Answer
The concentration of \( K^+ \) ions in the resulting solution is **0.200 M**.