Question

Use the average atomic masses given inside the front cover of this book to calculate the mass in grams of each of the following samples. a. 0.251 mole of lithium b. 1.51 moles of aluminum c. \(8.75 \times 10^{-2}\) moles of lead d. 125 moles of chromium e. \(4.25 \times 10^{3}\) moles of iron f. 0.000105 mole of magnesium

Short answer

The mass of each sample in grams is as follows: a. 1.74 g of lithium b. 40.74 g of aluminum c. 18.13 g of lead d. 6499.5 g of chromium e. 237342.125 g of iron f. 0.00255 g of magnesium

Step-by-step solution

a. 0.251 mole of lithium

Average atomic mass of Lithium (Li) = 6.94 g/mol To find the mass of 0.251 moles of lithium: mass (Li) = moles × average atomic mass mass (Li) = 0.251 mol × 6.94 g/mol = 1.74 g

b. 1.51 moles of aluminum

Average atomic mass of Aluminum (Al) = 26.98 g/mol To find the mass of 1.51 moles of aluminum: mass (Al) = moles × average atomic mass mass (Al) = 1.51 mol × 26.98 g/mol = 40.74 g

c. \(8.75 \times 10^{-2}\) moles of lead

Average atomic mass of lead (Pb) = 207.2 g/mol To find the mass of \(8.75 \times 10^{-2}\) moles of lead: mass (Pb) = moles × average atomic mass mass (Pb) = \(8.75 \times 10^{-2}\) mol × 207.2 g/mol = 18.13 g

d. 125 moles of chromium

Average atomic mass of Chromium (Cr) = 51.996 g/mol To find the mass of 125 moles of chromium: mass (Cr) = moles × average atomic mass mass (Cr) = 125 mol × 51.996 g/mol = 6499.5 g

e. \(4.25 \times 10^{3}\) moles of iron

Average atomic mass of Iron (Fe) = 55.845 g/mol To find the mass of \(4.25 \times 10^{3}\) moles of iron: mass (Fe) = moles × average atomic mass mass (Fe) = \(4.25 \times 10^{3}\) mol × 55.845 g/mol = 237342.125 g

f. 0.000105 mole of magnesium

Average atomic mass of Magnesium (Mg) = 24.305 g/mol To find the mass of 0.000105 moles of magnesium: mass (Mg) = moles × average atomic mass mass (Mg) = 0.000105 mol × 24.305 g/mol = 0.00255 g

Key concepts

Average Atomic Mass

The average atomic mass of an element is an essential concept in chemistry because it allows us to calculate the mass of atoms in grams effectively. It represents the weighted average mass of the atoms in a naturally occurring element, often mentioned in the periodic table. This value is particularly useful when dealing with isotopes, which are variations of the same element with different numbers of neutrons. When you need to determine the average atomic mass, you consider the mass of each isotope and its relative abundance. Multiply these two numbers together for each isotope, and then sum up these values. This provides you with the average atomic mass that you can use in calculations such as converting moles to grams, just as in the original exercise
When looking at lithium, for example, its average atomic mass is quoted as 6.94 g/mol. This is a weighted average considering its isotopes and their abundance in nature. By understanding this concept, you can determine the mass in grams for any amount of substance when given the moles.

Stoichiometry

Stoichiometry is the part of chemistry that involves the calculation of reactants and products in chemical reactions. It allows chemists to predict how much product will form from a given amount of reactants or vice versa. This area of study is deeply rooted in the mole concept and the balanced chemical equation, as the coefficients in these equations tell us the ratio in which substances react or are produced.
In our exercise, stoichiometry principles help determine the mass of different elements given their moles. By using the average atomic mass and the number of moles provided, you can scale the calculations to find the desired quantity in grams. The equation, mass = moles × average atomic mass, is a classic example of a stoichiometric calculation that helps in converting moles to grams
This allows a better understanding of chemical reactions by providing quantitative information that is necessary for practical chemical synthesis.

Mole Concept

The mole is a fundamental unit in chemistry that measures the amount of substance. One mole contains exactly Avogadro's number of particles, which is approximately \(6.022 \, \times \, 10^{23}\). This enormous number helps chemists count and quantify atoms, molecules, ions, and other particles involved in practical and theoretical chemistry.
The exercise demonstrates the mole concept by requiring the conversion of a chemical amount in moles to grams. To do this conversion, you need the average atomic mass of the element, which tells you the mass of one mole of that element in grams. For instance, the calculation 0.251 mol of lithium using its average atomic mass of 6.94 g/mol shows how the mole serves as a bridge between the microscopic world of atoms and macroscopic measurements we can see and use.
Understanding the mole concept is key to grasping chemical quantities and making accurate predictions about chemical processes, such as sizing of reactants and yield estimations in synthesis.