Zinc Content In Brass: A Quantitative Analysis
Hey guys! Today, we're diving deep into a quantitative chemistry problem that involves calculating the percentage of zinc in a brass sample. This is a classic type of problem you might encounter in chemistry, and it's super practical because it helps us understand the composition of different materials. Let's break it down step by step to make sure we understand every part of the process.
Setting Up the Problem
So, here's the scenario: We have a 5-gram sample of brass, which, as you might know, is an alloy mainly made up of copper and zinc. This sample is reacted with hydrochloric acid (HCl). The reaction produces hydrogen gas, and we collect 0.689 dm³ of it under standard conditions. Our mission, should we choose to accept it (and we totally do!), is to find out the percentage by mass of zinc in the brass sample. To start, it's really important to recognize that only zinc reacts with hydrochloric acid to produce hydrogen gas. Copper doesn't participate in this reaction, which simplifies our calculations quite a bit. This is a key piece of information that helps us isolate the role of zinc in the reaction. We need to use the given volume of hydrogen gas to figure out how much zinc reacted, and then we can calculate the percentage of zinc in the original brass sample. Remember, the end goal is to express zinc's contribution as a percentage of the total mass of the brass. This kind of problem is a fantastic way to sharpen our stoichiometry skills and apply the principles of chemical reactions to real-world scenarios. Understanding these reactions is crucial not only for exams but also for various applications in material science and engineering.
Writing the Balanced Chemical Equation
Alright, let's get to the nitty-gritty! The first thing we need to do when tackling a problem like this is to write out the balanced chemical equation. This is the foundation upon which all our calculations will be built. The reaction between zinc (Zn) and hydrochloric acid (HCl) produces zinc chloride (ZnClâ‚‚) and hydrogen gas (Hâ‚‚). So, the unbalanced equation looks like this:
Zn + HCl → ZnCl₂ + H₂
Now, we need to make sure that the number of atoms for each element is the same on both sides of the equation. Looking at the equation, we can see that we have one zinc atom on each side, which is great. However, we have one hydrogen atom and one chlorine atom on the left side, but two hydrogen atoms and two chlorine atoms on the right side. To balance this, we need to put a coefficient of 2 in front of the HCl. This gives us:
Zn + 2 HCl → ZnCl₂ + H₂
Now, if we count the atoms, we have one zinc atom, two hydrogen atoms, and two chlorine atoms on both sides. So, the equation is balanced! This balanced equation is super important because it tells us the molar ratios of the reactants and products. In this case, it tells us that one mole of zinc reacts with two moles of hydrochloric acid to produce one mole of zinc chloride and one mole of hydrogen gas. This 1:1 molar ratio between zinc and hydrogen gas is going to be crucial for our next steps. Remember, balancing the equation correctly is paramount because if the ratios are off, the entire calculation will be incorrect. So, always double-check your work!
Converting Volume of Hydrogen Gas to Moles
Now that we have our balanced equation, the next step is to figure out how many moles of hydrogen gas were produced in the reaction. We were given the volume of hydrogen gas (0.689 dm³) at standard conditions. Standard conditions, or STP (Standard Temperature and Pressure), are defined as 0°C (273.15 K) and 1 atmosphere (atm) of pressure. At STP, one mole of any ideal gas occupies a volume of 22.4 dm³. This is a fundamental concept in chemistry, and it's going to help us convert the volume of hydrogen gas into moles. To do this, we can use the ideal gas law, but since we're at STP, we can use a simple conversion factor. We know that 1 mole of gas occupies 22.4 dm³ at STP. So, we can set up a proportion to find the number of moles of hydrogen gas:
Moles of H₂ = (Volume of H₂) / (Molar volume at STP) Moles of H₂ = (0.689 dm³) / (22.4 dm³/mol)
When we do the math, we get:
Moles of H₂ ≈ 0.0308 moles
So, approximately 0.0308 moles of hydrogen gas were produced in the reaction. This value is absolutely crucial because, according to our balanced equation, the number of moles of hydrogen gas produced is equal to the number of moles of zinc that reacted. This is the bridge that connects the amount of hydrogen gas we measured to the amount of zinc in our brass sample. Understanding this conversion and the principles behind it is essential for mastering stoichiometry. Make sure you're comfortable with this step before moving on!
Calculating Moles of Zinc
Okay, so we've figured out that we produced approximately 0.0308 moles of hydrogen gas. Now comes the really cool part: using the stoichiometry of the reaction to determine how many moles of zinc reacted. Remember our balanced chemical equation:
Zn + 2 HCl → ZnCl₂ + H₂
This equation tells us that for every 1 mole of zinc (Zn) that reacts, 1 mole of hydrogen gas (Hâ‚‚) is produced. It's a simple 1:1 molar ratio. This is incredibly helpful because it means the number of moles of hydrogen gas we calculated is exactly the same as the number of moles of zinc that reacted. Therefore:
Moles of Zn = Moles of H₂ Moles of Zn ≈ 0.0308 moles
That's it! We've determined that about 0.0308 moles of zinc reacted with the hydrochloric acid. This step is super important because it links the experimental measurement (volume of hydrogen gas) to the amount of zinc in our original sample. It's a direct application of the principles of stoichiometry, and it highlights the power of balanced chemical equations in quantitative analysis. Understanding these molar ratios is key to solving a wide range of chemistry problems, so make sure you've got this concept down pat. We are really making strides now in figuring out the mass of zinc in our brass sample, which is our next logical step.
Converting Moles of Zinc to Grams
Alright, we're on the home stretch now! We know the number of moles of zinc that reacted (0.0308 moles), and our next step is to convert this into grams. To do this, we're going to need the molar mass of zinc. The molar mass is the mass of one mole of a substance, and it's usually expressed in grams per mole (g/mol). You can find the molar mass of zinc on the periodic table. It's approximately 65.38 g/mol. So, one mole of zinc weighs 65.38 grams. To convert moles to grams, we simply multiply the number of moles by the molar mass:
Mass of Zn = (Moles of Zn) × (Molar mass of Zn) Mass of Zn = (0.0308 moles) × (65.38 g/mol)
When we do the calculation, we get:
Mass of Zn ≈ 2.01 grams
So, there are approximately 2.01 grams of zinc in the brass sample that reacted with the hydrochloric acid. This is a significant result because it tells us the actual mass of zinc present in our 5-gram sample. We're getting closer and closer to finding the percentage of zinc, which is our final goal. Remember, this conversion from moles to grams is a fundamental skill in chemistry, and it's used all the time in various calculations. It's all about using the molar mass as a bridge between the mole world and the gram world. With this mass of zinc in hand, we're ready to calculate the percentage composition.
Calculating the Percentage of Zinc in the Brass Sample
Okay, guys, the moment we've been working towards! We're finally ready to calculate the percentage of zinc in the brass sample. We know that the mass of zinc in the sample is approximately 2.01 grams, and we know that the total mass of the brass sample is 5 grams. To find the percentage of zinc, we'll use the following formula:
Percentage of Zn = (Mass of Zn / Total mass of brass sample) × 100% Percentage of Zn = (2.01 g / 5 g) × 100%
Let's plug in the numbers and do the math:
Percentage of Zn = (0.402) × 100% Percentage of Zn ≈ 40.2%
So, the brass sample contains approximately 40.2% zinc by mass. And there you have it! We've successfully calculated the percentage composition of zinc in the brass sample. This final step really ties everything together, showing how all the previous calculations lead to the answer we were seeking. It's super rewarding when you can take a problem from start to finish and get a meaningful result. This skill of calculating percentage composition is crucial in many areas of chemistry and material science, as it helps us understand the makeup of different materials. Pat yourselves on the back, folks – we nailed it!
Conclusion
Alright, team, we've reached the end of our journey through this quantitative chemistry problem! We started with a 5-gram brass sample, reacted it with hydrochloric acid, collected the hydrogen gas produced, and then, using a series of calculations, determined that the sample contains approximately 40.2% zinc by mass. That's quite an accomplishment! We covered a lot of ground, from balancing chemical equations to converting between moles and grams, and finally calculating percentage composition. This type of problem really highlights the importance of stoichiometry and how it connects the macroscopic world (grams and volumes) to the microscopic world (moles and atoms). Remember, the key to solving these types of problems is to break them down into smaller, manageable steps. Start with the balanced chemical equation, then use the information given in the problem to calculate the number of moles of reactants and products. From there, you can convert to grams or volumes as needed, and finally, calculate the desired percentage or concentration. Most importantly, practice makes perfect! The more problems you solve, the more comfortable you'll become with these concepts. So, keep at it, guys, and you'll be quantitative chemistry pros in no time! Thanks for joining me on this chemical adventure. Keep exploring, keep learning, and I'll catch you in the next one!