Question

Calculate the potassium ion in grams per litre after mixing 100 ml of 0.250 M kcl and 200 ml of 0.100 M K2SO4

Answer 1

[AI-generated answer — Bot GPT-4o]

To determine the potassium ion concentration in grams per litre after mixing the two solutions, you'll need to do the following steps:

1. Calculate the moles of potassium ions from each solution.
2. Determine the volume of the mixed solution in litres.
3. Calculate the total concentration of potassium ions in the mixed solution.
4. Convert the concentration from moles per litre to grams per litre.

### Step 1: Calculate Moles of Potassium Ions

#### For KCl:
\[
\text{Volume of } KCl = 100 \text{ ml} = 0.100 \text{ L}
\]
\[
\text{Concentration of } KCl = 0.250 \text{ M}
\]
\[
\text{Moles of } KCl = \text{Volume} \times \text{Concentration} = 0.100 \text{ L} \times 0.250 \text{ M} = 0.025 \text{ moles}
\]
Each KCl molecule provides 1 potassium ion (K^+), so:
\[
\text{Moles of } K^+ \text{ from } KCl = 0.025 \text{ moles}
\]

#### For K2SO4:
\[
\text{Volume of } K2SO4 = 200 \text{ ml} = 0.200 \text{ L}
\]
\[
\text{Concentration of } K2SO4 = 0.100 \text{ M}
\]
\[
\text{Moles of } K2SO4 = \text{Volume} \times \text{Concentration} = 0.200 \text{ L} \times 0.100 \text{ M} = 0.020 \text{ moles}
\]
Each K2SO4 molecule provides 2 potassium ions (2 K^+), so:
\[
\text{Moles of } K^+ \text{ from } K2SO4 = 2 \times 0.020 \text{ moles} = 0.040 \text{ moles}
\]

### Step 2: Calculate the Total Volume of the Mixed Solution
\[
\text{Total Volume} = 100 \text{ ml} + 200 \text{ ml} = 300 \text{ ml} = 0.300 \text{ L}
\]

### Step 3: Calculate the Total Moles of Potassium Ions
\[
\text{Total moles of } K^+ = \text{Moles from KCl} + \text{Moles from K2SO4} = 0.025 \text{ moles} + 0.040 \text{ moles} = 0.065 \text{ moles}
\]

### Step 4: Concentration in Moles per Litre
\[
\text{Concentration of } K^+ \text{ ions} = \frac{\text{Total moles of } K^+}{\text{Total volume in litres}} = \frac{0.065 \text{ moles}}{0.300 \text{ L}} = 0.217 \text{ M}
\]

### Step 5: Convert Concentration to Grams per Litre

The molar mass of potassium (K) is approximately 39.1 g/mol.

\[
\text{Concentration of K}^+ \text{ in grams per litre} = \text{Concentration in moles per litre} \times \text{Molar mass of K}
\]
\[
= 0.217 \, \text{M} \times 39.1 \, \text{g/mol} \approx 8.4867 \, \text{g/L}
\]

Therefore, the concentration of potassium ions in the mixed solution is approximately **8.49 g/L**.