Stock Solution Calculations A Step By Step Guide For Ammonium Sulfate

$$

Hey everyone! Today, we're diving deep into the world of stock solutions, specifically focusing on a problem involving ammonium sulfate ${ (NH_4)_2 SO_4 }$. Stock solutions are the backbone of many experiments in chemistry, biology, and even cooking! They allow us to create solutions of known concentrations, which we can then dilute to get the exact concentrations we need for our work. So, let's break down this problem step by step, making sure we understand each concept along the way.

Understanding the Stock Solution Basics

Before we jump into the calculations, let's get a solid grasp on what a stock solution actually is. Stock solutions are essentially concentrated solutions that we prepare in advance. Think of it like making a strong coffee concentrate – you wouldn't drink it straight, but you'd dilute it with water to get your desired cup of joe. In the lab, we do the same thing. We create a concentrated stock solution, and then dilute it to the working concentration needed for our experiments. This saves us time and reduces the chances of making errors each time we need a specific concentration.

Why are Stock Solutions Important?

• Efficiency: Imagine having to weigh out tiny amounts of chemicals every time you need a solution. That's not only tedious but also increases the risk of measurement errors. Stock solutions streamline this process.
• Accuracy: By starting with a larger, more easily measurable amount of solute, we can create a stock solution with a high degree of accuracy. Diluting this stock then allows us to achieve precise working concentrations.
• Time-Saving: Preparing stock solutions in advance saves valuable time, especially in labs where many solutions are used regularly.
• Consistency: Using stock solutions ensures consistency across experiments, as the starting concentration is always the same.

Key Concepts to Remember

• Molarity (M): This is the most common way to express concentration in chemistry. It's defined as the number of moles of solute per liter of solution (mol/L).
• Moles (mol): This is a unit of measurement for the amount of a substance. One mole contains Avogadro's number ${ (6.022 \times 10^{23}) }$ of particles (atoms, molecules, ions, etc.).
• Molar Mass (g/mol): This is the mass of one mole of a substance. You can calculate it by adding up the atomic masses of all the atoms in the chemical formula.
• Dilution: This is the process of reducing the concentration of a solution by adding more solvent (usually water). The key principle here is that the number of moles of solute remains constant during dilution.

Problem Breakdown: Dissolving ${ (NH_4)_2 SO_4 }$ to Create a Stock Solution

Okay, now let's tackle the problem at hand. We're given that 66.05 g of ${ (NH_4)_2 SO_4 }$ (ammonium sulfate) is dissolved in enough water to make 250 mL of solution. Then, a 10.0 mL sample of this solution is diluted to 50.0 mL. Our goal is to figure out the concentration of the final diluted solution. To do this, we need to break it down into manageable steps.

Step 1: Calculate the Molar Mass of ${ (NH_4)_2 SO_4 }$

This is our first crucial step. We need to know the molar mass of ammonium sulfate to convert the mass we have (66.05 g) into moles. Let's break down the chemical formula:

• Nitrogen (N): There are 2 N atoms, each with an atomic mass of approximately 14.01 g/mol.
• Hydrogen (H): There are 8 H atoms (2 x 4), each with an atomic mass of approximately 1.01 g/mol.
• Sulfur (S): There is 1 S atom with an atomic mass of approximately 32.07 g/mol.
• Oxygen (O): There are 4 O atoms, each with an atomic mass of approximately 16.00 g/mol.

Now, let's calculate the molar mass:

Molar Mass = (2 * 14.01) + (8 * 1.01) + 32.07 + (4 * 16.00)
Molar Mass = 28.02 + 8.08 + 32.07 + 64.00
Molar Mass = 132.17 g/mol

So, the molar mass of ${ (NH_4)_2 SO_4 }$ is approximately 132.17 g/mol. This is a key value that we'll use in the next step.

Step 2: Calculate the Molarity of the Stock Solution

Now that we know the molar mass, we can calculate the molarity of the initial stock solution. Remember, molarity (M) is moles of solute per liter of solution. We have the mass of solute (66.05 g) and the volume of the solution (250 mL), so let's convert these to the correct units and calculate the molarity.

First, let's convert grams to moles:

Moles = Mass / Molar Mass
Moles = 66.05 g / 132.17 g/mol
Moles ≈ 0.500 mol

Next, let's convert milliliters to liters:

Liters = Milliliters / 1000
Liters = 250 mL / 1000
Liters = 0.250 L

Now we can calculate the molarity:

Molarity = Moles / Liters
Molarity = 0.500 mol / 0.250 L
Molarity = 2.00 M

So, the molarity of the stock solution is 2.00 M. This means there are 2.00 moles of ${ (NH_4)_2 SO_4 }$ in every liter of this solution.

Step 3: Calculate the Molarity of the Diluted Solution

This is where the dilution equation comes into play. The dilution equation is a simple but powerful tool that helps us calculate concentrations after dilution. It's based on the principle that the number of moles of solute remains constant during dilution. The equation is:

M1V1 = M2V2

Where:

• M1 = Molarity of the stock solution
• V1 = Volume of the stock solution used for dilution
• M2 = Molarity of the diluted solution (what we want to find)
• V2 = Volume of the diluted solution

In our problem, we have:

• M1 = 2.00 M (from Step 2)
• V1 = 10.0 mL
• V2 = 50.0 mL
• M2 = ? (This is what we need to calculate)

Let's plug these values into the equation and solve for M2:

(2.00 M) * (10.0 mL) = M2 * (50.0 mL)
20.0 = 50.0 * M2
M2 = 20.0 / 50.0
M2 = 0.400 M

Therefore, the molarity of the diluted solution is 0.400 M. That's our final answer!

Key Takeaways and Best Practices for Working with Solutions

Alright, guys, we've successfully navigated this stock solution problem! But before we wrap up, let's recap some key takeaways and best practices for working with solutions in the lab.

Double-Check Your Calculations:

• Accuracy is paramount when preparing solutions. Always double-check your calculations, especially when dealing with molar masses and dilutions. A small error in calculation can lead to significant discrepancies in your final concentration.

Use Appropriate Glassware:

• Volumetric flasks are your best friend for preparing solutions of known concentrations. These flasks are specifically calibrated to hold a precise volume at a specific temperature. Using graduated cylinders for final volume adjustments can introduce errors.
• For dilutions, use calibrated pipettes to accurately measure the volume of the stock solution you're transferring.

Mix Thoroughly:

• Ensure complete dissolution of the solute by mixing the solution thoroughly. Use a stir bar and a magnetic stirrer for larger volumes, or invert the flask multiple times for smaller volumes. Inadequate mixing can lead to concentration gradients within the solution.

Label Clearly:

• Always label your solutions with the name of the solute, the concentration, the date of preparation, and your initials. This prevents mix-ups and ensures that you can track the age of your solutions.

Store Properly:

• Store solutions in appropriate containers and under conditions that maintain their stability. Some solutions may be light-sensitive or air-sensitive, so use amber bottles or store them under an inert atmosphere.

Consider Error Propagation:

• Be aware of error propagation in multi-step calculations. If you have uncertainties in your initial measurements, these uncertainties will propagate through your calculations and affect the final result. Consider using significant figures appropriately to reflect the precision of your measurements.

Practice Makes Perfect:

• Like any skill in the lab, preparing solutions becomes easier with practice. Don't be afraid to ask for guidance and clarification from your instructor or colleagues.

By following these best practices, you'll be well-equipped to prepare accurate and reliable solutions for your experiments.

Conclusion

So, there you have it! We've walked through a detailed solution to a stock solution problem, calculated the molar mass and molarity, and even touched on some best practices for solution preparation. Remember, understanding these fundamental concepts is crucial for success in chemistry and related fields. Keep practicing, and you'll become a solution-making pro in no time! If you have any questions, feel free to ask. Happy experimenting, guys!