While interning in a biology lab over the summer, you are asked to prepare a KCl solution with a molar concentration 0.52 mol/L accurate to within 0.01 mol/L. You have many beakers and flasks to measure volume to arbitrary precision, but only one balance that measures mass to the nearest  0.1 g. What minimum volume of solution should you prepare? Looking online you find that the molecular weight of KCl is 74.55 g/mol.

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.

While interning in a biology lab over the summer, you are asked to prepare a KCl solution with a molar concentration 0.52 mol/L accurate to within 0.01 mol/L. You have many beakers and flasks to measure volume to arbitrary precision, but only one balance that measures mass to the nearest 0.1 g. What minimum volume of solution should you prepare? Looking online you find that the molecular weight of KCl is 74.55 g/mol.

Learn how to calculate the minimum volume needed to prepare a KCl solution with a concentration of 0.52 mol/L, considering measurement uncertainties. This solution explains the core concepts of molarity, uncertainty in measurements, and the relevant formulas. Suitable for introductory chemistry or physics students.

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