Helium Pressure Change: Volume Tripled At Constant Temp
Hey guys! Let's dive into a fascinating chemistry problem involving helium gas. We're going to explore how the pressure of helium changes when we mess with its volume, keeping the temperature steady. This is a classic example of Boyle's Law in action. So, let's break it down step by step and make sure we understand every bit of it. Ready? Let’s get started!
Understanding the Problem
So, here's the deal: We've got some helium gas hanging out at 25 degrees Celsius. The initial volume of this gas is 2 liters, and it's exerting a pressure of 0.6 atmospheres. Now, imagine we decide to triple the volume of the gas while keeping the temperature the same. The big question is, what happens to the pressure? More specifically, we want to know the final pressure in centimeters of mercury (cmHg). This involves understanding the relationship between pressure and volume when the temperature is constant.
Key Concepts: Boyle's Law
The key here is Boyle's Law. This law states that for a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional. In simpler terms, if you increase the volume, the pressure decreases, and vice versa. It’s like squeezing a balloon – if you make it smaller (decrease the volume), the air inside pushes harder (increase the pressure).
Mathematically, Boyle's Law is expressed as:
P₁V₁ = P₂V₂
Where:
- P₁ is the initial pressure,
- V₁ is the initial volume,
- P₂ is the final pressure,
- V₂ is the final volume.
This equation is our bread and butter for solving this problem. It tells us exactly how the pressure and volume are related when the temperature isn't changing. Make sure you understand this, guys, because it’s crucial for many gas-related problems!
Initial Conditions
Let’s identify our initial conditions. This is like gathering all the ingredients before we start cooking. We know:
- Initial Volume (V₁) = 2 liters
- Initial Pressure (P₁) = 0.6 atmospheres
- The volume is tripled, so the Final Volume (V₂) = 3 * V₁ = 3 * 2 liters = 6 liters
- The temperature remains constant, which is important because Boyle's Law applies only when the temperature doesn’t change.
Now, we have all the pieces we need to plug into our equation. It's like having all the puzzle pieces laid out – now we just need to fit them together!
Solving for the Final Pressure
Alright, let's use Boyle's Law to find the final pressure (P₂). We've got our equation:
P₁V₁ = P₂V₂
We need to rearrange this equation to solve for P₂. It’s like a bit of algebraic maneuvering, but nothing too scary. Divide both sides by V₂:
P₂ = (P₁V₁) / V₂
Now, we plug in the values we know:
P₂ = (0.6 atm * 2 L) / 6 L
P₂ = 1.2 atm / 6
P₂ = 0.2 atmospheres
So, the final pressure is 0.2 atmospheres. That wasn't too bad, right? But hold on, we’re not quite done yet!
Converting Units: Atmospheres to cmHg
The question asks for the final pressure in centimeters of mercury (cmHg), but we've calculated it in atmospheres. No sweat, we just need to do a quick unit conversion. Think of it like translating from one language to another.
We know that:
1 atmosphere = 76 cmHg
So, to convert 0.2 atmospheres to cmHg, we multiply:
P₂ (in cmHg) = 0.2 atm * 76 cmHg/atm
P₂ (in cmHg) = 15.2 cmHg
There we have it! The final pressure of the helium gas is 15.2 cmHg. Awesome!
Step-by-Step Solution
Let’s recap the entire solution step by step. This is super helpful for reinforcing what we’ve learned. Think of it as a mini-review session.
- Identify the Knowns:
- Initial Volume (V₁) = 2 liters
- Initial Pressure (P₁) = 0.6 atmospheres
- Final Volume (V₂) = 6 liters (3 times the initial volume)
- Apply Boyle's Law:
- P₁V₁ = P₂V₂
- Rearrange the Equation to Solve for P₂:
- P₂ = (P₁V₁) / V₂
- Plug in the Values:
- P₂ = (0.6 atm * 2 L) / 6 L
- P₂ = 0.2 atmospheres
- Convert Atmospheres to cmHg:
- P₂ (in cmHg) = 0.2 atm * 76 cmHg/atm
- P₂ (in cmHg) = 15.2 cmHg
So, step-by-step, we've got it all figured out. Remember, breaking down a problem into smaller steps makes it way easier to tackle.
Common Mistakes to Avoid
Let’s chat about some common slip-ups people make when solving problems like this. Avoiding these mistakes can save you a lot of headaches. Trust me, we've all been there!
- Forgetting the Units: Always, always, always include units in your calculations. It's like the grammar of math and science. If you forget the units, you might end up with a number that doesn't make sense. For example, mixing up liters and milliliters can throw everything off.
- Not Converting Units: In this problem, we needed to convert atmospheres to cmHg. Failing to do this conversion would give you the wrong final answer. Always double-check what units the question is asking for.
- Misunderstanding Boyle's Law: Boyle's Law only works when the temperature and the amount of gas are constant. If the temperature changes, you’ll need to use a different gas law, like the combined gas law. Keep this in mind, guys!
- Algebra Errors: Sometimes, the biggest mistakes happen when rearranging equations or plugging in numbers. Take your time and double-check your work. It’s like proofreading an essay – a quick review can catch silly errors.
Real-World Applications of Boyle's Law
Okay, so we’ve solved the problem, but where does this stuff actually matter in the real world? Boyle's Law isn't just some abstract concept; it's used in tons of practical applications. Knowing these applications can make the whole concept feel more tangible and, dare I say, even cooler!
- Scuba Diving: Scuba divers need to understand Boyle's Law because the pressure changes dramatically as they descend into the water. The air in their lungs and equipment compresses as the pressure increases, and it expands as they ascend. This is why divers need to exhale continuously while ascending to avoid lung injuries. It's a matter of life and breath, literally!
- Medical Respirators: Medical respirators use Boyle's Law to deliver air to patients. The device adjusts the volume and pressure of the air to match the patient's needs. This ensures the right amount of oxygen is delivered safely and effectively. Think of it as Boyle's Law helping people breathe easier.
- Internal Combustion Engines: The engines in our cars rely on Boyle's Law to function. As the piston moves down in the cylinder, the volume increases, and the pressure decreases, drawing in the air-fuel mixture. When the piston moves up, the volume decreases, and the pressure increases, compressing the mixture before ignition. It’s a high-speed, high-pressure dance of gas laws!
- Weather Forecasting: Meteorologists use gas laws, including Boyle's Law, to predict weather patterns. Changes in atmospheric pressure are related to changes in volume and temperature, which can help forecast storms and other weather events. So, next time you check the weather, remember Boyle's Law is playing a part!
Practice Problems
Alright, guys, let’s flex those brain muscles with some practice problems! The best way to really nail a concept is to practice, practice, practice. So, grab a pen and paper, and let’s tackle these problems together.
Practice Problem 1
A gas occupies a volume of 5 liters at a pressure of 2 atmospheres. If the volume is increased to 10 liters at constant temperature, what is the new pressure?
Hint: Use Boyle's Law, P₁V₁ = P₂V₂.
Practice Problem 2
A balloon has a volume of 3 liters at standard atmospheric pressure (1 atm). If the pressure is increased to 3 atm while keeping the temperature constant, what is the new volume of the balloon?
Hint: Remember to rearrange Boyle's Law to solve for the new volume.
Practice Problem 3
5 liters of gas at 200 kPa pressure is expanded to 15 liters at constant temperature. Calculate the final pressure.
Hint: Make sure your units are consistent. You can use kPa directly with Boyle's Law.
Take your time to work through these problems. If you get stuck, go back and review the steps we discussed earlier. And don't worry, the more you practice, the easier it gets!
Conclusion
So, guys, we've taken a deep dive into a helium gas problem, tackled Boyle's Law, and even explored some real-world applications. We started with an initial set of conditions, figured out how pressure changes with volume at constant temperature, and converted units like pros. Remember, the key to mastering these concepts is understanding the underlying principles and practicing regularly.
Whether you're a student acing your chemistry class or just a curious mind exploring the world, understanding gas laws like Boyle's Law is super valuable. It's not just about memorizing equations; it’s about grasping how the world around us works. Keep exploring, keep questioning, and keep learning. You've got this!
