To prepare a potassium chloride (KCl) solution with a molar concentration of 0.52 mol/L, we need to ensure the concentration accuracy is within ±0.01 mol/L. The goal is to determine the minimum volume of solution to prepare, such that the uncertainty in the mass due to the balance (which measures to the nearest 0.1 g) does not exceed the allowable concentration variation.

Step 1: Expression for Molarity (Concentration)

The molarity $C$ is given by: $C = \frac{n}{V}$ where:

• $n$ is the number of moles of KCl,
• $V$ is the volume of the solution in liters.

The number of moles $n$ can also be expressed as: $n = \frac{m}{M}$ where:

• $m$ is the mass of KCl in grams,
• $M$ is the molar mass of KCl, which is 74.55 g/mol.

Thus, the concentration can be rewritten as: $C = \frac{m}{M \cdot V}$

Step 2: Uncertainty in Concentration

The mass is measured using a balance that measures to the nearest 0.1 g, so the uncertainty in the mass is $\pm 0.1 \, \text{g}$. This will affect the concentration as follows.

The uncertainty in concentration $\Delta C$ is related to the uncertainty in the mass $\Delta m = 0.1 \, \text{g}$ by the formula: $\Delta C = \frac{\Delta m}{M \cdot V}$

Given that the allowable uncertainty in concentration is $\pm 0.01 \, \text{mol/L}$, we set: $\frac{0.1 \, \text{g}}{74.55 \, \text{g/mol} \cdot V} = 0.01 \, \text{mol/L}$

Step 3: Solve for the Minimum Volume

Solving for $V$: $V = \frac{0.1}{74.55 \times 0.01} = \frac{0.1}{0.7455} \approx 0.134 \, \text{L}$

Thus, the minimum volume of solution you should prepare is approximately 0.134 L or 134 mL.

This ensures that the concentration can be accurate within ±0.01 mol/L, given the limitation of your balance.

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Would you like further details or have any questions? Here are some related queries:

1. How would the preparation change if the balance had a different precision?
2. What would be the new minimum volume if the target concentration was 1 mol/L?
3. How would you calculate the exact mass of KCl needed for 0.52 mol/L in 134 mL of solution?
4. What are some potential errors in preparing the KCl solution besides balance accuracy?
5. How does temperature affect the molar concentration of a solution?

Tip: When preparing solutions, always take into account the precision of your measuring instruments to minimize potential errors.