Problem 83 - Chemistry: Principles and Reactions

Question

A solution contains \(158.2 \mathrm{~g}\) of \(\mathrm{KOH}\) per liter; its density is \(1.13 \mathrm{~g} / \mathrm{mL}\). A lab technician wants to prepare \(0.250 \mathrm{~m} \mathrm{KOH}\), starting with \(100.0 \mathrm{~mL}\) of this solution. How much water or solid KOH should be added to the \(100.0-\mathrm{mL}\) portion?

Step-by-Step Solution

Answer

Answer: The technician should add 1.028 L (or 1028 mL) of water to the 100 mL KOH solution to achieve a concentration of 0.250 M KOH.

Step 1: Calculate the initial mass of KOH

Using the given mass concentration and volume, calculate the initial mass of KOH in the 100 mL portion. Mass concentration = 158.2 g/L Volume = 100.0 mL = 0.100 L (100 mL converted to liters) The initial mass of KOH = Mass concentration x Volume = 158.2 g/L x 0.100 L = 15.82 g Initially, we have 15.82 grams of KOH in 100 mL of the solution.

Step 2: Calculate the number of moles of KOH

Have the molar mass of KOH equal 56.1 g/mol Calculate the number of moles of KOH using the mass of KOH and its molar mass: Moles of KOH = Mass of KOH / Molar Mass (KOH) = 15.82 g / 56.1 g/mol = 0.282 mol Now, we know that there are 0.282 moles of KOH in the original solution.

Step 3: Determine the needed moles of KOH for final concentration

Now that we have to find how many moles would be needed to achieve the desired concentration of 0.250 M in the final solution: Desired concentration = 0.250 mol/L Original volume: 0.100 L Moles of KOH_required = Desired concentration x Original volume = 0.250 mol/L x 0.100 L = 0.025 mol To achieve the desired concentration of 0.250 M, we need 0.025 moles of KOH.

Step 4: Determine if KOH needs to be added or water

Compare the needed moles of KOH for the desired concentration with the available moles of KOH in the original solution: Needed moles of KOH: 0.025 mol Available moles of KOH: 0.282 mol Since there are already more moles of KOH (0.282 mol) in the original solution than required for the desired concentration (0.025 mol), there's no need to add solid KOH. Instead, the technician should add water.

Step 5: Calculate the final volume of the 0.250 M solution

Use the moles of KOH and the desired concentration to calculate the final volume of the solution: Final volume = Moles of KOH / Desired concentration = 0.282 mol / 0.250 mol/L = 1.128 L The final volume of the 0.250 M KOH solution is 1.128 L.

Step 6: Calculate the amount of water required

Subtract the initial volume (100 mL) from the final volume (1.128 L) to find the amount of water to be added: Amount of water required = Final volume - Initial volume = 1.128 L - 0.100 L = 1.028 L The technician should add 1.028 L (or 1028 mL) of water to the 100 mL KOH solution to achieve a concentration of 0.250 M KOH.

Key Concepts

Understanding Mass Concentration

Mass concentration refers to the amount of a substance (in grams, for example) that is dissolved in a specific volume of solution (often in liters). In this exercise, we are dealing with a mass concentration of potassium hydroxide (KOH), which is given as 158.2 grams per liter. Let's break it down a bit further so it becomes clearer:

• The unit 'grams per liter' (g/L) tells us how many grams of KOH are dissolved in each liter of solution.
• This measurement is crucial because it gives a direct indication of how "strong" or concentrated the solution is in terms of KOH content.
• In everyday terms, the higher the mass concentration, the more dense or packed with KOH molecules the solution is.
• Calculating the mass of KOH in smaller volumes, like 100 mL, simply involves adjusting for the proportional volume difference by multiplying the concentration by the volume in liters.

In our example, we calculated the mass of KOH in 100 mL or 0.1 L of the solution as 15.82 grams, using the given mass concentration of 158.2 g/L. This conversion helps us lay the foundation for calculating molarity and understanding solution properties more comprehensively.

Basics of Molarity Calculations

Molarity (M) is one of the most common ways to express concentration in chemistry. It represents the number of moles of a solute (in our case, KOH) per liter of solution. The process of calculating molarity involves two main steps:

• Determining the number of moles of the solute: This can be done by dividing the mass of the solute by its molar mass. For KOH, having a molar mass of 56.1 g/mol, we found that 15.82 g corresponds to 0.282 moles.
• Using the moles to calculate molarity: Once the moles are calculated, you can find the molarity by dividing the moles by the volume of the solution in liters. In our scenario, we desire a final molarity of 0.250 M for the KOH solution.

Calculating molarity helps us understand how "concentrated" a solution will be in terms of its ability to react with other substances. It's a critical step in preparing solutions for lab experiments, ensuring they meet the required specifications for chemical reactions.

Understanding the Dilution Process

Dilution is the process of reducing the concentration of a solute in a solution, usually by adding more solvent. The key purpose of dilution is to achieve a desired concentration. Here's how dilution works, relating to our example:

• Identifying the required concentration: Here, our target is to achieve a concentration of 0.250 M for the KOH solution.
• Comparing current versus desired concentration: We initially have 0.282 moles of KOH in 100 mL and want to adjust this to match the desired 0.025 moles for our target concentration.
• Adding water to achieve the desired concentration: Since the solution is more concentrated than required, we add water instead of more KOH. By calculating the final volume needed for 0.250 M, we determine how much additional water to add, eventually requiring 1.028 liters more to dilute it properly.

Dilution is a fundamental technique in chemistry and allows for precise control of solution concentrations. It plays a crucial role in laboratories where specific solution profiles are necessary for accurate experimental results.