Solving For Metal Sulfide Composition Identifying Me In Me2S3
Hey everyone! Today, we're diving into a fascinating chemistry problem that involves figuring out the identity of a metal in a sulfide compound. We've got some experimental data – 4.466 g of a metal reacting with 3.852 g of sulfur – and the empirical formula of the resulting compound, which is Me2S3. Our mission, should we choose to accept it (and we totally do!), is to pinpoint which metal 'Me' is. The options on the table are iron (Fe), sodium (Na), potassium (K), and calcium (Ca). So, buckle up, fellow chemistry enthusiasts, as we embark on this exciting journey of discovery!
Deciphering the Empirical Formula
Alright, let's start by cracking the code of the empirical formula, Me2S3. Remember, the empirical formula represents the simplest whole-number ratio of atoms in a compound. In this case, for every two atoms of our mystery metal (Me), there are three atoms of sulfur (S). This ratio is super important because it gives us a crucial piece of the puzzle for identifying the metal.
To figure out which metal Me is, we need to delve into the world of moles. Moles, you see, are the chemist's favorite unit for counting atoms and molecules. It's like saying, "Hey, I don't have just a bunch of atoms; I have a specific number of them, a mole of them!" Avogadro's number (approximately 6.022 x 10^23) defines a mole, which represents the number of entities present in one mole of a substance. So, we'll convert the given masses of the metal and sulfur into moles. This conversion requires the molar masses of the elements involved.
The molar mass of an element is essentially the mass of one mole of that element, and it conveniently corresponds to the element's atomic weight on the periodic table. For sulfur (S), the molar mass is approximately 32.06 g/mol. This means that one mole of sulfur atoms weighs about 32.06 grams. We'll use this information to convert the mass of sulfur in our compound into moles. Once we have the moles of sulfur, we can use the empirical formula to deduce the moles of the metal. The beauty of the empirical formula is that it provides a direct mole ratio between the elements in the compound. In our case, the Me2S3 formula tells us that the mole ratio of metal to sulfur is 2:3. This ratio will be the linchpin in determining the moles of the metal.
Converting Grams to Moles
The first step in our quest is to convert the masses of sulfur into moles. We know we have 3.852 g of sulfur, and we know the molar mass of sulfur is approximately 32.06 g/mol. So, we'll use this information to convert the mass of sulfur in our compound into moles.
To convert grams to moles, we'll use the following formula:
Moles = Mass (g) / Molar Mass (g/mol)
Plugging in the values for sulfur, we get:
Moles of S = 3.852 g / 32.06 g/mol ≈ 0.1201 mol
So, we have approximately 0.1201 moles of sulfur in our compound. Now, let's keep this value handy as we move on to the next step!
Leveraging the Empirical Formula Ratio
Now, the magic of the empirical formula comes into play! The empirical formula, Me2S3, tells us that for every 3 moles of sulfur (S), we have 2 moles of the metal (Me). This is a crucial ratio that will help us determine the moles of our mystery metal. Guys, this is where the problem starts to really come together.
We've already calculated that we have 0.1201 moles of sulfur in our compound. To find the moles of the metal, we'll use the mole ratio from the empirical formula:
(Moles of Metal) / (Moles of Sulfur) = 2 / 3
We can rearrange this equation to solve for the moles of the metal:
Moles of Metal = (2 / 3) * Moles of Sulfur
Plugging in the moles of sulfur we calculated earlier:
Moles of Metal = (2 / 3) * 0.1201 mol ≈ 0.08007 mol
So, we have approximately 0.08007 moles of our mystery metal in the compound. We're getting closer to unveiling the metal's identity!
Identifying the Metal
Okay, we've done the heavy lifting of converting masses to moles and using the empirical formula to find the moles of the metal. Now comes the exciting part: identifying the metal itself! To do this, we'll use another crucial piece of information – the mass of the metal that reacted, which is 4.466 g.
We now know the mass of the metal (4.466 g) and the number of moles of the metal (approximately 0.08007 mol). This is exactly what we need to calculate the molar mass of the metal. Remember, molar mass is the mass of one mole of a substance, and it's a unique property that can help us identify elements. The formula for molar mass is:
Molar Mass (g/mol) = Mass (g) / Moles (mol)
Let's plug in the values we have:
Molar Mass of Metal = 4.466 g / 0.08007 mol ≈ 55.78 g/mol
So, the molar mass of our mystery metal is approximately 55.78 g/mol. Now, we need to compare this value to the molar masses of the potential metals given in the options: iron (Fe), sodium (Na), potassium (K), and calcium (Ca). We can find these molar masses on the periodic table.
Comparing Molar Masses
Let's take a look at the molar masses of the potential metals:
- Iron (Fe): Approximately 55.845 g/mol
- Sodium (Na): Approximately 22.99 g/mol
- Potassium (K): Approximately 39.10 g/mol
- Calcium (Ca): Approximately 40.08 g/mol
Comparing the molar mass we calculated (55.78 g/mol) to these values, we can see a striking similarity between our calculated molar mass and the molar mass of iron (Fe). The slight difference could be due to experimental errors or rounding during calculations. However, the closeness in value strongly suggests that our mystery metal is indeed iron!
The Verdict: Iron (Fe) is Our Metal!
After a thorough investigation involving stoichiometry, mole conversions, and molar mass calculations, we've successfully unmasked our mystery metal. The evidence points convincingly to iron (Fe) as the metal that reacts with sulfur to form the compound Me2S3. This whole process, guys, really shows how powerful chemistry can be in figuring out the world around us.
Wrapping Up
So, to recap, we started with the masses of the metal and sulfur, the empirical formula of the compound (Me2S3), and a mission to identify the metal. We converted grams to moles, used the empirical formula to find the mole ratio, calculated the molar mass of the metal, and compared it to the molar masses of the given options. Through this journey, we confidently concluded that the metal is iron (Fe).
This problem is a classic example of how stoichiometry and the concept of moles are used in chemistry to determine the composition of compounds. It's a fundamental skill that every aspiring chemist needs to master. Keep practicing, guys, and you'll become chemistry sleuths in no time!
If you enjoyed this chemical quest, stay tuned for more exciting explorations in the world of chemistry. There's always something new to discover, and the possibilities are as endless as the elements themselves. Keep experimenting, keep questioning, and most importantly, keep having fun with chemistry!
