Identify Gas In Cylinder: Density At 15°C & 0.97atm

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Identifying a Pure Monatomic Gas Using Density: A Chemistry Experiment

Hey guys! Ever wondered how chemists figure out what's inside a mysterious cylinder of gas? Well, it's a fascinating process that combines careful measurements with some good ol' chemistry knowledge. Let's dive into a scenario where a chemistry student is on a mission to identify a pure monatomic gas. They've collected a sample and found its density to be 5.38 g/L under specific conditions: a temperature of 15°C and a pressure of 0.97 atm. How do we use this information to crack the case? Let's break it down step by step.

Understanding the Ideal Gas Law

First things first, we need to bring in the big guns: the Ideal Gas Law. This law is a cornerstone of chemistry and helps us relate pressure, volume, temperature, and the number of moles of a gas. The formula looks like this:

PV = nRT

Where:

  • P is the pressure (in atm)
  • V is the volume (in liters)
  • n is the number of moles
  • R is the ideal gas constant (0.0821 L·atm/mol·K)
  • T is the temperature (in Kelvin)

But wait, we have density, not the number of moles! No sweat, we can tweak this equation to include density. Remember that density (d) is mass (m) per unit volume (V):

d = m/V

And the number of moles (n) is mass (m) divided by molar mass (M):

n = m/M

Let's substitute these into the Ideal Gas Law. We get:

PV = (m/M)RT

Rearranging to solve for density (d = m/V), we have:

P = (d/M)RT

And finally, solving for molar mass (M):

M = (dRT)/P

This is the golden equation we'll use! It relates the molar mass of the gas to its density, pressure, and temperature. Now, let's plug in the values from our chemistry student's experiment.

Calculations: Finding the Molar Mass

Alright, time to put on our calculation hats! We know:

  • Density (d) = 5.38 g/L
  • Pressure (P) = 0.97 atm
  • Temperature (T) = 15°C

But hold on! Temperature needs to be in Kelvin. To convert from Celsius to Kelvin, we add 273.15:

T(K) = T(°C) + 273.15

T(K) = 15 + 273.15 = 288.15 K

Now we have all the pieces of the puzzle. Let's plug the values into our molar mass equation:

M = (dRT)/P

M = (5.38 g/L * 0.0821 L·atm/mol·K * 288.15 K) / 0.97 atm

M ≈ 131.3 g/mol

So, the molar mass of the gas is approximately 131.3 g/mol. This is a crucial piece of information!

Identifying the Gas: Comparing Molar Masses

Okay, we've got the molar mass. What does that tell us? Well, the molar mass is like a fingerprint for elements and compounds. Each element has a unique molar mass, which you can find on the periodic table. Since we know our gas is monatomic (meaning it's made of single atoms), we can compare our calculated molar mass to the molar masses of monatomic gases like helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn).

Here are the approximate molar masses of these gases:

  • Helium (He): 4 g/mol
  • Neon (Ne): 20 g/mol
  • Argon (Ar): 40 g/mol
  • Krypton (Kr): 84 g/mol
  • Xenon (Xe): 131 g/mol
  • Radon (Rn): 222 g/mol

Comparing our calculated molar mass (131.3 g/mol) to this list, we see a very close match with Xenon (Xe), which has a molar mass of 131 g/mol. Therefore, it's highly likely that the gas in the cylinder is Xenon! It's always a good idea to consider potential sources of error, but given the close match, Xenon is the most plausible answer.

Potential Sources of Error

Now, before we declare victory, let's think about potential sources of error in this experiment. No measurement is perfect, and there are always factors that can influence the results. Here are a few things to consider:

  • Accuracy of Measurements: Were the temperature and pressure measured accurately? Even small errors in these measurements can affect the calculated molar mass.
  • Gas Purity: Was the gas sample truly pure? If there were other gases mixed in, it would throw off the density measurement and, consequently, the molar mass calculation.
  • Ideal Gas Law Limitations: The Ideal Gas Law works best under ideal conditions (low pressure and high temperature). If the gas deviates significantly from ideal behavior, the calculated molar mass might not be entirely accurate.

To minimize these errors, it's crucial to use calibrated instruments, ensure the gas sample is as pure as possible, and be aware of the limitations of the Ideal Gas Law. If higher accuracy is needed, more sophisticated techniques and equations of state might be necessary.

Why This Matters: Real-World Applications

So, why is all this important? Identifying gases has numerous real-world applications across various fields. Here are a few examples:

  • Industrial Chemistry: In chemical plants, it's essential to identify the gases involved in different processes for safety and efficiency.
  • Environmental Monitoring: Identifying atmospheric gases helps monitor pollution levels and understand climate change.
  • Medical Applications: Analyzing the composition of exhaled breath can help diagnose medical conditions.
  • Scientific Research: Identifying gases is crucial in many scientific experiments, from studying chemical reactions to exploring the properties of new materials.

By understanding how to identify gases using basic principles like the Ideal Gas Law and density measurements, we gain valuable insights into the world around us and contribute to advancements in various fields. Pretty cool, huh?

Conclusion: The Power of Chemistry

So, there you have it! By carefully measuring the density of a gas sample and applying the Ideal Gas Law, our chemistry student was able to identify the gas as Xenon. This example highlights the power of chemistry to unlock the secrets of the universe, one molecule at a time. It also underscores the importance of accurate measurements and critical thinking in scientific investigations. Remember, chemistry is not just about memorizing formulas; it's about understanding the underlying principles and applying them to solve real-world problems. Keep exploring, keep experimenting, and keep asking questions! Who knows what exciting discoveries you'll make next? This process involves understanding fundamental concepts, performing accurate measurements, and applying the ideal gas law. By determining the density of the gas at a specific temperature and pressure, it becomes possible to calculate its molar mass and subsequently identify the gas by comparing it with known values. This method showcases how basic principles in chemistry can be used to solve practical problems and identify unknown substances, emphasizing the importance of chemistry in various scientific and industrial applications. Chemistry combines detailed measurements with established chemical principles. The student uses the Ideal Gas Law to determine the gas's molar mass from its density, pressure, and temperature. This reveals the gas's unique identity, which is essential in various scientific and industrial fields for safety, efficiency, and discovery. Understanding the gas’s properties leads to real-world applications, solidifying chemistry's role in solving practical problems and making new findings. The process teaches how to measure accurately and think critically in science, demonstrating that chemistry helps understand and solve real-world challenges. So, keep learning and experimenting. There's no limit to what you can discover!