Question

Which of the following is a \(0.500 \mathrm{M} \mathrm{KCl}\) solution? (a) \(0.500 \mathrm{g} \mathrm{KCl} / \mathrm{mL}\) solution; (b) \(36.0 \mathrm{g} \mathrm{KCl} / \mathrm{L}\) solu- tion; (c) 7.46 mg KCl/mL solution; (d) 373 g KCl in 10.00 L solution

Short answer

The 0.500 M KCl solution is option (d) - 373 g KCl in 10.00 L solution.

Step-by-step solution

Calculation for option (a)

For option (a), we are given the mass of KCl in grams per mL of solution. However, neither of these can be directly converted to moles per liter. The data makes no sense and is incorrect for a molar solution.

Calculation for option (b)

For option (b), we are given the mass of KCl in grams per litre. To convert this to moles per liter (i.e., molarity), we divide the mass by the molar mass of KCl (which is approximately 74.55 g/mol). That gives \((36.0 \mathrm{g} \mathrm{KCl} / \mathrm{L})/74.55 \mathrm{g/mol} = 0.483 \mathrm{M}\). Therefore, option (b) is not a 0.500 M KCl solution.

Calculation for option (c)

For option (c), we are given the mass of KCl in milligrams per mL of solution. We can convert milligrams to grams and mL to L to get the molarity: \((7.46 \mathrm{mg} \mathrm{KCl}/\mathrm{mL}) * \mathrm{1g/1000mg} * \mathrm{1000mL/1L} = 7.46 \mathrm{g} \mathrm{KCl} / \mathrm{L} \). Then, divide this by the molar mass of KCl (74.55 g/mol) to get the molarity: \(7.46 \mathrm{g} / 74.55 \mathrm{g/mol} = 0.100 \mathrm{M}\). Therefore, option (c) is not a 0.500 M KCl solution.

Calculation for option (d)

Finally, for option (d), we have 373 g of KCl in 10.00 L of solution. To get molarity, again divide the mass by the molar mass of KCl, and then by the volume of the solution in liters: \( (373 \mathrm{g} / 74.55 \mathrm{g/mol}) / 10.00 \mathrm{L} = 0.500 \mathrm{M}\). Therefore, option (d) is a 0.500 M KCl solution.

Key concepts

KCl solution

A KCl solution refers to a homogeneous mixture made by dissolving potassium chloride (KCl) in a liquid, typically water. Potassium chloride is a white crystalline compound, and when dissolved, it dissociates into potassium ions (\(K^+\)) and chloride ions (\(Cl^-\)). This process occurs because water molecules surround the ions, facilitating their separation, and forming a uniform solution.
KCl solutions are commonly used in laboratories and medical settings. In laboratories, they are applied in experiments requiring specific ionic strengths or reactions involving potassium. In medicine, KCl solutions can be used in oral or intravenous treatments to replenish potassium levels. It's important to know the concentration of KCl in a solution for accurate application, as even a slight change can significantly impact reactions or medical outcomes.
Here are a few important points about KCl solutions:

• The preparation involves careful measurement of KCl and solvent, often adjusting based on the desired molarity.
• They should be stored properly to prevent contamination or concentration changes.
• Molarity, which is moles of solute per liter of solution, plays a critical role in defining how strong or weak a solution is.

molar mass

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a substance, typically expressed in grams per mole (\( ext{g/mol}\)). For potassium chloride (KCl), the molar mass is approximately 74.55 g/mol. To calculate the molar mass, add the atomic masses of each element within a compound according to the chemical formula. For KCl, add the atomic mass of potassium (around 39.10) and the atomic mass of chlorine (around 35.45).
Understanding molar mass is crucial for various calculations:

• It allows conversion between grams and moles, facilitating concentration calculations.
• It helps predict how substances will react and the quantities needed for reactions.
• It enhances precision in laboratory settings, especially when preparing solutions to a specified molarity.

Accurate knowledge of molar mass ensures precise experimental and practical applications, such as when preparing a KCl solution where an exact molarity is required to achieve the desired effect.

concentration calculation

Calculating concentration, especially molarity, involves finding how much solute is present in a given volume of solution. Molarity (\( ext{M}\)) is calculated as the number of moles of solute divided by liters of solution, \( ext{M} = rac{ ext{moles of solute}}{ ext{liters of solution}} \).
Here's a step-by-step method to calculate the concentration of a KCl solution:

• Start with the mass of KCl. Convert this mass to moles using the molar mass of KCl (74.55 g/mol).
• Measure the total volume of the solution in liters.
• Divide the number of moles by the volume in liters to find the molarity.

For example, if you dissolve 373 g of KCl in 10 liters of water, first convert grams to moles (\(rac{373}{74.55}\)) and then divide by the volume (10), giving a molarity of \(0.500 ext{M}\).
Correct concentration calculation is indispensable in many fields, including chemistry, biology, and pharmacology, ensuring desired reactions and proper dosages in solutions and mixtures.