Question

\(100 \mathrm{ml}\) of \(0.2 \mathrm{M} \mathrm{K}_{2} \mathrm{SO}_{4}\) is diluted with \(100 \mathrm{ml}\) of water. The \(\mathrm{K}^{+}\) ion in the solution (1) \(0.4 \mathrm{M}\) (2) \(0.1 \mathrm{M}\) (3) \(0.2 \mathrm{M}\) (4) \(0.8 \mathrm{M}\)

Short answer

The concentration of \({\text{K}^+}\) in the solution is 0.2 M.

Step-by-step solution

- Understand the problem

We need to determine the concentration of \({\text{K}^+}\) ions after diluting a \({0.2 \text{M} \text{K}_{2} \text{SO}_{4}}\) solution.

- Determine initial moles of \({\text{K}_{2} \text{SO}_{4}}\)

Calculate the moles of \({\text{K}_{2} \text{SO}_{4}}\) in the initial solution (100 mL of 0.2 M). Use the formula: \(\text{Moles} = \text{Concentration} \times \text{Volume}\footnote{Volume should be in Litres} = 0.2 \text{mol/L} \times 0.1 \text{L} = 0.02 \text{mol}\text{K}_{2} \text{SO}_{4}\).

- Considering dilution effect

The solution is diluted with an equal volume of water (100 mL). This will double the total volume to 200 mL (or 0.2 L).

- Calculate new concentration of \({\text{K}_{2} \text{SO}_{4}}\) after dilution

Use the formula for concentration: \(\text{New Concentration} = \frac{\text{Moles of Solute}}{\text{Total Volume}} = \frac{0.02 \text{mol} }{0.2 \text{L}} = 0.1 \text{M} \text{K}_{2} \text{SO}_{4}\).

- Determine \({\text{K}^+}\) ions concentration

Each formula unit of \({\text{K}_{2} \text{SO}_{4}}\) provides 2 \({\text{K}^+}\) ions. Thus, the concentration of \({\text{K}^+}\) ions is twice the concentration of \({\text{K}_{2} \text{SO}_{4}}\), so \(\text{Concentration of } \text{K}^{+} = 2 \times 0.1 \text{M} = 0.2 \text{M}\).

Key concepts

Molarity

Molarity is a measure of concentration, indicating the number of moles of a solute per liter of solution. It’s denoted by the symbol ‘M’. Understanding molarity is crucial for solving chemical calculation problems. To calculate molarity, use the formula: \[ \text{Molarity} (M) = \frac{\text{Moles of Solute}}{\text{Volume of Solution in Liters}} \] For instance, if we dissolve 0.2 moles of potassium sulfate (\text{K}_2\text{SO}_4) in 1 liter of water, the molarity is 0.2 M. The correct calculation and understanding of molarity help us determine concentrations needed for various chemical reactions and solutions.

Dilution

Dilution reduces the concentration of a solute in a solution by adding more solvent. When diluting, the number of moles of solute remains the same; however, the overall volume of the solution increases. The formula for the effect of dilution is given by: \[ \text{M}_1 \times \text{V}_1 = \text{M}_2 \times \text{V}_2 \] Here, \text{M}_1 and \text{V}_1 are the initial molarity and volume, while \text{M}_2 and \text{V}_2 are the new molarity and volume after dilution. In our problem, diluting 100 mL of 0.2 M \text{K}_2\text{SO}_4 with 100 mL of water gives a total volume of 200 mL, leading to a new molarity calculation. Dilution helps in achieving desired concentrations for various laboratory and industrial processes.

Ion Concentration

Ion concentration refers to the amount of ions present in a solution. In our exercise, each molecule of potassium sulfate (\text{K}_2\text{SO}_4) dissociates into 2 potassium ions (\text{K}^+) and 1 sulfate ion (\text{SO}_4^{2-}) in solution. To find the concentration of these ions: \[\text{Ion Concentration} = n \times \text{Molarity of the Compound} \] where 'n' is the number of ions per formula unit. Given the 0.1 M solution of \text{K}_2\text{SO}_4 after dilution, the concentration of \text{K}^+ ions becomes: \[2 \times 0.1 \text{M} = 0.2 \text{M} \] Understanding ion concentration is pivotal in reactions where ions are the active participants.

Chemical Calculations

Chemical calculations involve using quantitative approaches to determine various properties, such as concentrations, amounts, and proportions in chemical reactions. Here are key steps:

• Identify the given values and what you need to find.
• Use appropriate formulas based on the chemical principles involved.
• Carry out step-by-step calculations, ensuring correct units and significant figures.

For the exercise: 1. Calculate moles of \text{K}_2\text{SO}_4: \[ \text{Moles} = 0.2 \text{M} \times 0.1 \text{L} = 0.02 \text{mol} \] 2. Find new concentration after dilution given total volume: \[0.02 \text{mol} / 0.2 \text{L} = 0.1 \text{M} \text{K}_2\text{SO}_4 \] 3. Determine ion concentrations based on dissociation. Mastery of such calculations enables accurate predictions and adjustments in chemical experiments.