Determine Empirical Formula From Combustion: A Chemistry Guide

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Hey everyone! Let's dive into a fascinating problem in organic chemistry: figuring out the empirical formula of an organic substance when we're given data from its combustion. This might sound intimidating, but trust me, we'll break it down step by step. We're going to use a practical example, so you can follow along and really understand the process. We'll tackle this with a friendly approach, so you can think of me as your study buddy guiding you through the chemistry maze!

The Problem: Deconstructing the Compound

So, we're given that a 5.12 g sample of an organic substance is burned completely. The resulting gaseous mixture contains 0.24 moles of carbon dioxide (CO₂), 1.8 g of water vapor (H₂O), and 448 mL of nitrogen gas (N₂) at standard conditions. Our mission, should we choose to accept it (and we do!), is to:

a. Determine the empirical formula of this mysterious organic substance.

Let’s put on our detective hats and start piecing together the puzzle! Remember, the empirical formula tells us the simplest whole-number ratio of atoms in a compound. To find it, we need to figure out the number of moles of each element (Carbon, Hydrogen, and Nitrogen in this case) present in the original substance.

Step 1: Cracking the Carbon Code

The first clue we have is the amount of CO₂ produced. Since each CO₂ molecule contains one carbon atom, the number of moles of carbon in the original substance is equal to the number of moles of CO₂ produced. We know we have 0.24 moles of CO₂, so:

  • Moles of Carbon (C) = 0.24 moles

See? We're making progress already! This is like finding the first piece of a jigsaw puzzle. Let's keep going!

Step 2: Decoding the Hydrogen Hint

Next up, we have water (H₂O). Each water molecule contains two hydrogen atoms. We're given 1.8 g of H₂O, so we need to convert this mass into moles. To do that, we'll use the molar mass of water, which is approximately 18 g/mol:

  • Moles of H₂O = 1.8 g / 18 g/mol = 0.1 moles

Since each mole of H₂O has 2 moles of Hydrogen, we can say:

  • Moles of Hydrogen (H) = 0.1 moles H₂O * 2 = 0.2 moles

Awesome! We've uncovered another piece of the puzzle. We now know how much carbon and hydrogen we have.

Step 3: Unraveling the Nitrogen Enigma

Now for the nitrogen (N₂). We're given the volume of N₂ gas at standard conditions (448 mL). To find the number of moles, we'll use the ideal gas law, but a simpler way at standard conditions is to remember that 1 mole of any gas occupies 22.4 L (or 22400 mL). So,

  • Moles of N₂ = 448 mL / 22400 mL/mol = 0.02 moles

Since we're interested in the amount of nitrogen atoms, and each N₂ molecule has two nitrogen atoms:

  • Moles of Nitrogen (N) = 0.02 moles N₂ * 2 = 0.04 moles

Fantastic! We've successfully determined the number of moles of nitrogen. This feels like cracking a secret code, doesn't it?

Step 4: Oxygen – The Missing Link?

Now, you might be thinking, “What about oxygen?” It’s a crucial element in organic compounds, but the problem doesn't directly give us the amount of oxygen produced. This is where we need to be a bit clever. We'll use the conservation of mass principle.

We know the total mass of the original substance (5.12 g). We also know the moles (and thus mass) of carbon, hydrogen, and nitrogen. If we add up the masses of these elements and subtract that from the total mass of the substance, we can find the mass of oxygen.

First, let’s calculate the masses of carbon, hydrogen, and nitrogen:

  • Mass of Carbon = 0.24 moles * 12 g/mol = 2.88 g
  • Mass of Hydrogen = 0.2 moles * 1 g/mol = 0.2 g
  • Mass of Nitrogen = 0.04 moles * 14 g/mol = 0.56 g

Now, let's add these up:

  • Total mass of C, H, N = 2.88 g + 0.2 g + 0.56 g = 3.64 g

Now, subtract this from the total mass of the original substance to get the mass of oxygen:

  • Mass of Oxygen = 5.12 g - 3.64 g = 1.48 g

Finally, convert the mass of oxygen to moles:

  • Moles of Oxygen (O) = 1.48 g / 16 g/mol = 0.0925 moles

Woohoo! We've found the moles of oxygen. This was like finding the keystone in an arch, everything is falling into place now!

Step 5: Finding the Simplest Ratio

We now have the number of moles of each element: C (0.24), H (0.2), N (0.04), and O (0.0925). To find the empirical formula, we need to find the simplest whole-number ratio between these moles. To do this, we'll divide each mole value by the smallest mole value, which is 0.04:

  • C: 0.24 / 0.04 = 6
  • H: 0.2 / 0.04 = 5
  • N: 0.04 / 0.04 = 1
  • O: 0.0925 / 0.04 ≈ 2.31

We're almost there! We have C₆H₅N₁O₂.₃₁. But wait! We need whole numbers. To get rid of the decimal, we can multiply all the ratios by a factor that turns 2.31 into a whole number. Multiplying by 4 gets us close (2.31 * 4 = 9.24, which is nearly 9), and then adjusting from there, we see that we could multiply each number by a factor to bring all the numbers to the near whole number. If we look carefully at Oxygen moles ratio we can see that it's very near to 9/4 and thus we can multiply each number by 4. We get whole number ratios:

  • C: 6 * 4 = 24
  • H: 5 * 4 = 20
  • N: 1 * 4 = 4
  • O: 2.31 * 4 ≈ 9

So, the empirical formula is C₂₄H₂₀N₄O₉. This is our final answer! Feels good to have solved the puzzle, doesn’t it?

Wrapping Up: Key Takeaways

So, guys, we've successfully determined the empirical formula of an organic substance from combustion data. We followed these crucial steps:

  1. Calculated moles of each element (C, H, N) from the combustion products (CO₂, H₂O, N₂).
  2. Determined the mass of oxygen by using the conservation of mass principle.
  3. Converted the mass of oxygen to moles.
  4. Found the simplest whole-number ratio of the moles of each element.

This process might seem like a lot of work, but each step is logical and brings us closer to the solution. Practice makes perfect, so try tackling similar problems to solidify your understanding. Remember, chemistry is like a puzzle – challenging, but incredibly rewarding when you find the solution! Keep up the awesome work, and happy solving!