Question

Use the average atomic masses given inside the front cover of this book to calculate the number of moles of each element present in each of the following samples. a. 21.50 g of arsenic b. \(9.105 \mathrm{g}\) of phosphorus c. \(0.05152 \mathrm{g}\) of barium d. \(43.15 \mathrm{g}\) of carbon e. \(26.02 \mathrm{g}\) of chromium f. \(1.951 \mathrm{g}\) of platinum

Short answer

The number of moles for each element is as follows: a. Arsenic: \(0.287 \mathrm{mol}\) b. Phosphorus: \(0.294 \mathrm{mol}\) c. Barium: \(0.000375 \mathrm{mol}\) d. Carbon: \(3.59 \mathrm{mol}\) e. Chromium: \(0.500 \mathrm{mol}\) f. Platinum: \(0.0100 \mathrm{mol}\)

Step-by-step solution

Find the average atomic mass of arsenic

Using the periodic table, we find that the average atomic mass of arsenic (As) is 74.92 g/mol.

Calculate the number of moles of arsenic

Now, use the formula: Number of moles = (mass of the sample) / (average atomic mass) Number of moles \(= \frac{21.50 \mathrm{g}}{74.92 \mathrm{g/mol}} = 0.287 \mathrm{mol} \) There are 0.287 moles of arsenic in the sample. b. 9.105 g of phosphorus:

Find the average atomic mass of phosphorus

Using the periodic table, we find that the average atomic mass of phosphorus (P) is 30.97 g/mol.

Calculate the number of moles of phosphorus

Now, use the formula: Number of moles \(= \frac{9.105 \mathrm{g}}{30.97 \mathrm{g/mol}} = 0.294 \mathrm{mol} \) There are 0.294 moles of phosphorus in the sample. c. 0.05152 g of barium:

Find the average atomic mass of barium

Using the periodic table, we find that the average atomic mass of barium (Ba) is 137.33 g/mol.

Calculate the number of moles of barium

Now, use the formula: Number of moles \(= \frac{0.05152 \mathrm{g}}{137.33 \mathrm{g/mol}} = 0.000375 \mathrm{mol} \) There are 0.000375 moles of barium in the sample. d. 43.15 g of carbon:

Find the average atomic mass of carbon

Using the periodic table, we find that the average atomic mass of carbon (C) is 12.01 g/mol.

Calculate the number of moles of carbon

Now, use the formula: Number of moles \(= \frac{43.15 \mathrm{g}}{12.01 \mathrm{g/mol}} = 3.59 \mathrm{mol} \) There are 3.59 moles of carbon in the sample. e. 26.02 g of chromium:

Find the average atomic mass of chromium

Using the periodic table, we find that the average atomic mass of chromium (Cr) is 51.996 g/mol.

Calculate the number of moles of chromium

Now, use the formula: Number of moles \(= \frac{26.02 \mathrm{g}}{51.996 \mathrm{g/mol}} = 0.500 \mathrm{mol} \) There are 0.500 moles of chromium in the sample. f. 1.951 g of platinum:

Find the average atomic mass of platinum

Using the periodic table, we find that the average atomic mass of platinum (Pt) is 195.08 g/mol.

Calculate the number of moles of platinum

Now, use the formula: Number of moles \(= \frac{1.951 \mathrm{g}}{195.08 \mathrm{g/mol}} = 0.0100 \mathrm{mol} \) There are 0.0100 moles of platinum in the sample.

Key concepts

Average Atomic Mass

When studying chemistry, the concept of average atomic mass plays a crucial role in mole calculations. Atomic mass is the mass of an atom, usually expressed in atomic mass units (amu). Since elements can have multiple isotopes—variations of the same element with different numbers of neutrons—chemists use the average atomic mass. This average takes into account the different isotopes and their relative abundances. For example, chlorine has isotopes like chlorine-35 and chlorine-37. The average atomic mass is a weighted average, not a simple mean. You can find this value on the periodic table and it helps predict how an element behaves in reactions.

The atomic mass average allows chemists to estimate how much of a substance you'll need for a certain amount of product in a reaction, making it a key concept in calculating moles.

Periodic Table

The periodic table is your go-to tool for finding properties of elements, like atomic masses needed for mole calculations. Organized by increasing atomic number, each element's atomic number represents the number of protons in its nucleus. Elements are grouped based on similar chemical properties, which makes it easier to predict their behavior in chemical reactions.

Key features of the periodic table:

• Rows are called periods and columns are groups or families.
• Elements in the same group have similar properties and valence electron configurations.
• Each element square typically shows the element symbol, atomic number, and average atomic mass.

Understanding how to use the periodic table helps you quickly locate important information like the average atomic mass, enabling precise calculations involving molarity and moles.

Mass to Moles Conversion

Converting mass to moles is a vital skill in chemistry for understanding the quantity of substance you have. The mole is a standard SI unit that represents a specific number of particles, usually atoms or molecules, in a given sample.

The conversion formula is simple: \[\text{Number of moles} = \frac{\text{mass of the sample (g)}}{\text{average atomic mass (g/mol)}}\]This calculation uses the mass of your sample and the element's average atomic mass to determine the number of moles. Essentially, it translates mass into a count of atoms or molecules.

Here’s a quick guide:

• Find the element's average atomic mass on the periodic table, measured in grams per mole.
• Use this as the denominator in your conversion formula, with your sample's mass as the numerator.
• By dividing, you calculate how many moles of atoms are in your sample.

Using this method, you can easily convert mass to moles, making predictions in chemical reactions much more accurate and consistent.