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Bot GPT-4o Sure, let's start by defining the terms:
### Molarity
Molarity (M) is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. It is represented by the formula:
\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \]
### Morality
It seems like *morality* is mentioned, but I believe the correct term you're looking for is *Molality*. Molality (m) is another measure of solution concentration, defined as the number of moles of solute per kilogram of solvent. It is represented by the formula:
\[ \text{Molality (m)} = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \]
### Calculate the concentration of Potassium Ion
First, we need to understand how many moles of potassium ions are present in both solutions and then calculate the total volume and concentration.
#### Step 1: Calculate moles of potassium ions
1. **For \( KCl \):**
\[ \text{M} = 0.250 \, \text{M} \]
\[ \text{Volume} = 100 \, \text{ml} = 0.100 \, \text{L} \]
Moles of \( KCl \):
\[ \text{moles of } KCl = 0.250 \, \text{M} \times 0.100 \, \text{L} = 0.025 \, \text{moles} \]
Since \( KCl \) dissociates into \( K^+ \) and \( Cl^- \), the moles of \( K^+ \) from \( KCl \) are:
\[ \text{moles of } K^+ = 0.025 \, \text{moles} \]
2. **For \( K_2SO_4 \):**
\[ \text{M} = 1 \, \text{M} \]
\[ \text{Volume} = 200 \, \text{ml} = 0.200 \, \text{L} \]
Moles of \( K_2SO_4 \):
\[ \text{moles of } K_2SO_4 = 1 \, \text{M} \times 0.200 \, \text{L} = 0.200 \, \text{moles} \]
Since \( K_2SO_4 \) dissociates into \( 2K^+ \) and \( SO_4^{2-} \), the moles of \( K^+ \) from \( K_2SO_4 \) are:
\[ \text{moles of } K^+ = 2 \times 0.200 = 0.400 \, \text{moles} \]
#### Step 2: Calculate total moles of potassium ions
Total moles of \( K^+ \):
\[ \text{Total moles of } K^+ = 0.025 \, \text{moles} + 0.400 \, \text{moles} = 0.425 \, \text{moles} \]
#### Step 3: Calculate total volume of the mixed solution
Combining the volumes:
\[ \text{Total Volume} = 100 \, \text{ml} + 200 \, \text{ml} = 300 \, \text{ml} = 0.300 \, \text{L} \]
#### Step 4: Calculate molarity of potassium ion
Molarity of \( K^+ \):
\[ \text{Molarity of } K^+ = \frac{\text{total moles of } K^+}{\text{total volume}} = \frac{0.425 \, \text{moles}}{0.300 \, \text{L}} \approx 1.417 \, \text{M} \]
#### Step 5: Convert the molarity to grams per liter
Molarity to grams per liter for potassium ion (\( K \)):
- Molar mass of \( K \) is approximately 39.1 g/mol.
Concentration in g/L:
\[ \text{Concentration of } K^+ = 1.417 \, \text{M} \times 39.1 \, \text{g/mol} = 55.43 \, \text{g/L} \]
So, the concentration of potassium ion (\( K^+ \)) in the mixed solution is approximately **55.43 grams per liter**.