Question

Formula Mass and the Mole Concept for Compounds How many molecules (or formula units) are in each sample? $$\begin{array}{lllll}{\text { a. } 85.26 \mathrm{gCCl}_{4}} & {\text { b. } 55.93 \mathrm{kg} \mathrm{NaHCO}_{3}} \\ {\mathrm{c} .119 .78 \mathrm{g} \mathrm{C}_{4} \mathrm{H}_{10}} & {\text { d. } 4.59 \times 10^{5} \mathrm{g} \mathrm{Na}_{3} \mathrm{PO}_{4}}\end{array}$$

Short answer

a. 3.34 * 10\(^{23}\) molecules of CCl\(_4\), b. 5.94 * 10\(^{26}\) formula units of NaHCO\(_3\), c. 1.56 * 10\(^{24}\) molecules of C\(_4\)H\(_10\), d. 7.72 * 10\(^{26}\) formula units of Na\(_3\)PO\(_4\).

Step-by-step solution

Calculate the Molar Mass of Each Compound

Using the periodic table, find the atomic masses for each element in the compound and multiply by the number of atoms of that element in the formula to get the molar mass. For example, for CCl\(_4\), the molar mass is C (12.01 g/mol) + 4 * Cl (4 * 35.45 g/mol) = 153.81 g/mol. Repeat this for each compound.

Convert Grams to Moles

Use the formula: number of moles = mass (g) / molar mass (g/mol) to convert the given mass of each compound to moles. For example, for 85.26 g of CCl\(_4\), the moles are 85.26 g / 153.81 g/mol.

Calculate Number of Molecules or Formula Units

Multiply the number of moles by Avogadro's number (6.022 * 10\(^{23}\) molecules/mol) to find the number of molecules or formula units. For CCl\(_4\), multiply the moles obtained in Step 2 by Avogadro's number.

Repeat Steps 2 and 3 for Other Compounds

Repeat the calculation of moles and the number of molecules or formula units for each of the other compounds given in the exercise.

Key concepts

Calculating Molar Mass

To kick off our journey into the world of chemistry, let's tackle the concept of molar mass. Picture this: every element has its unique weight, which is like its signature in the chemical universe. This weight is what we call atomic mass and you can find it listed in the periodic table for each element.

When we talk about molar mass, we're basically asking, 'If I had 6.022 x 10²³ (which is Avogadro's number, but more on that later) of these atoms, how much would they weigh?' This amount is one mole, and its weight in grams is the molar mass. So, how do we calculate this for a compound? It's like a baking recipe; first, note down the molar mass of each ingredient (element), then count how many of each ingredient you need, and voila—you add them up. If you see a compound like CCl₄, start with carbon. One carbon atom has a molar mass of 12.01 g/mol. Chlorine's molar mass is 35.45 g/mol, but since we have four chlorine atoms, we multiply this by four. Add these together, and you have the molar mass of CCl₄: 12.01 g/mol + (4 x 35.45 g/mol) = 153.81 g/mol.

Conversion of Grams to Moles

Now that we've calculated the molar mass, it's time to connect the dots between the mass of a substance we have in grams and the number of moles. Think of moles as a bridge that helps us cross from the tangible world of grams into the molecular realm, where chemists love to hang out!

So, how do we build this bridge? Simple: we use the formula you've likely scribbled in the margins of your notebook—moles = mass (g) divided by molar mass (g/mol). Let's say you have a treasure of 85.26 g of pure CCl₄. According to our recipe book (the molar mass calculation), CCl₄ weighs 153.81 g/mol. By dividing the grams we have by the molar mass, 85.26 g / 153.81 g/mol, we find out how many moles of CCl₄ we're dealing with. This step is like the magic spell that turns grams into moles, opening up a world of possibilities in stoichiometry.

Avogadro's Number

Here's a big hero in chemistry: Avogadro's number. The name might sound like someone you'd encounter in an Italian opera, but it's actually a super important constant in chemistry. Avogadro's number is a colossal figure, 6.022 x 10²³, and represents the number of particles (usually atoms or molecules) in one mole of a substance.

But why is it such a big deal? Well, think of it like this. You have countless molecules dancing around in even the tiniest speck of a compound. Avogadro's number lets us wrangle that almost infinite count into something manageable—a mole. So, when chemists say a mole, they're really talking about 6.022 x 10²³ particles of that substance. This number lets us translate between the world of the very small—the atomic scale—and the more familiar scale of grams and kilograms that we use in the lab.

Chemical Formula Units

Diving deeper into the world of chemistry, we encounter chemical formula units. These are the blueprints that tell us what's in a compound and how much. A formula unit of table salt, NaCl, says there's one sodium (Na) and one chlorine (Cl) atom for each unit. But what about larger or more complex structures?

For example, take sodium bicarbonate, NaHCO₃: there's one sodium, one hydrogen, one carbon, and three oxygen atoms per formula unit. Knowing this, you can calculate the mass of one mole, or Avogadro's number of formula units, the same way you'd find the molar mass. It's a neat little package of information that serves as the bedrock for calculations in chemistry.