Unlocking Boyle's Law: Volume Changes in Ideal Gases

What volume will an ideal gas occupy at 0.40 atmosphere if it originally occupies 0.50 liters at 0.20 atmosphere?

• A. 0.25 L
• B. 0.50 L
• C. 1 L
• D. 2 L

Answer: (A)

To determine the volume that an ideal gas will occupy when the pressure changes while keeping the temperature constant, we can apply Boyle's Law. Boyle's Law states that the volume of a gas is inversely proportional to its pressure when the temperature is held constant. This relationship can be expressed mathematically as: P1V1 = P2V2 where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. In this scenario, we begin with the initial conditions: the gas occupies 0.50 liters at a pressure of 0.20 atmospheres. The final pressure is 0.40 atmospheres, and we need to find the new volume (V2). Using Boyle's Law, we can rearrange the formula to solve for V2: V2 = (P1V1) / P2 Substituting the known values into the equation: - P1 = 0.20 atm - V1 = 0.50 L - P2 = 0.40 atm Now, substituting in the numbers: V2 = (0.20 atm * 0.50 L) / 0.40 atm V

Boyle's Law can feel like a tricky concept at first, but once you get your head around it, it's like catching the rhythm of a catchy song. You know what I mean? Let's break it down together.

Imagine you have an ideal gas sitting in a container. It occupies 0.50 liters at a pressure of 0.20 atmospheres. Now, life happens, right? Maybe someone increases the pressure to 0.40 atmospheres, and you're left wondering—what happens to the volume? That's where Boyle’s Law swoops in to save the day!

Boyle’s Law states that the volume (V) of a gas is inversely proportional to its pressure (P) when the temperature is held constant. So, this means if you increase the pressure, you should expect the volume to shrink, like a balloon that’s being squeezed. You can express this relationship mathematically with the formula:

P1V1 = P2V2

It sounds a bit like algebra homework, but hang in there! Here’s how we can break this down:

• P1 and V1 are your initial pressure and volume, and P2 and V2 are your final pressure and volume.

• In our case, we know:

• P1 = 0.20 atm

• V1 = 0.50 L

• P2 = 0.40 atm

You might be wondering, “Okay, but how do I find V2?” Let’s rearrange the formula to isolate V2:

V2 = (P1V1) / P2

Now, let’s plug in the numbers:

V2 = (0.20 atm * 0.50 L) / 0.40 atm

Now, just do a little math magic!

V2 = 0.10 L / 0.40 atm = 0.25 L

So, there you go! The new volume that our gas occupies when under increased pressure is 0.25 liters. You can almost visualize the gas getting squeezed into a smaller space.

This is a fundamental concept in both physics and chemistry, especially if you're gearing up for exams in nursing or other health sciences. Mastering these principles isn’t just about passing tests; it’s about understanding how things work at the molecular level, which is crucial in a healthcare setting.

And let’s face it, the better you understand these gas laws, the better prepared you’ll be for whatever comes your way in your nursing curriculum. It’s a win-win! So keep practicing with examples like these, because mastering the basics will help you soar to new heights in your studies.

You’re capable of so much more than you think. Just remember, each equation you tackle and each concept you grasp is a step closer to becoming a skilled nursing professional.