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Chapter 3: Problem 1

The atomic mass of \(\mathrm{Cl}\) is 35.45 amu, and the atomic mass of Al is 26.98 amu. What are the masses in grams of 3 mol of Al atoms and of \(2 \mathrm{~mol}\) of \(\mathrm{Cl}\) atoms?

Short Answer

Expert verified
The mass of 3 mol of Al is 80.94 g, and the mass of 2 mol of Cl is 70.90 g.

Step by step solution

01

- Understand the Molar Mass Concept

The molar mass relates atomic mass units (amu) to grams per mole (g/mol). For instance, the molar mass of Al (atomic mass 26.98 amu) is 26.98 g/mol, meaning one mole of Al atoms weighs 26.98 grams. Similarly, the molar mass of Cl (atomic mass 35.45 amu) is 35.45 g/mol.
02

- Calculate Mass of Al Atoms

We need to calculate the mass of 3 moles of Al atoms. Use the formula: \[\text{Mass} = \text{Number of moles} \times \text{Molar mass}\]Substituting the given values: \[\text{Mass of Al} = 3 \text{ mol} \times 26.98 \text{ g/mol} = 80.94 \text{ g}\]
03

- Calculate Mass of Cl Atoms

Next, calculate the mass of 2 moles of Cl atoms. Use the same formula: \[\text{Mass} = \text{Number of moles} \times \text{Molar mass}\]Substituting the given values: \[\text{Mass of Cl} = 2 \text{ mol} \times 35.45 \text{ g/mol} = 70.90 \text{ g}\]
04

- Verify Calculations

Check your work to ensure all calculations are correct: 3 moles of Al calculated to 80.94 grams and 2 moles of Cl calculated to 70.90 grams.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atomic Mass
Atomic mass is the mass of a single atom, measured in atomic mass units (amu). Each element has a unique atomic mass. The atomic mass of Aluminum (Al) is 26.98 amu, and for Chlorine (Cl), it is 35.45 amu. Atomic mass can be found on the periodic table. It reflects the weighted average of all isotopes of an element. Understanding atomic mass is essential, as it helps in calculating the molar mass and converting between atoms and grams.
Moles
A mole is a unit that measures the amount of a substance. One mole contains exactly 6.022 x 10^23 particles, such as atoms or molecules. This number is known as Avogadro's number. Moles link the microscopic world of atoms to the macroscopic world of grams and liters. For example, 1 mole of Al has 6.022 x 10^23 Al atoms. Similarly, 1 mole of Cl has the same number of Cl atoms. Using moles helps simplify calculations involving atoms and chemical reactions.
Molar Mass Calculation
Molar mass is the mass of one mole of a substance, measured in grams per mole (g/mol). It is numerically equal to the atomic mass but expressed in grams. To find the molar mass, use the atomic mass from the periodic table. For example, the molar mass of Al is 26.98 g/mol, as its atomic mass is 26.98 amu. Similarly, the molar mass of Cl is 35.45 g/mol. Knowing the molar mass allows you to convert moles to grams and vice versa using the formula: \[\text{Mass} = \text{Number of moles} \times \text{Molar mass}\]
Aluminum (Al) Atoms
Aluminum (Al) is a silvery-white metal known for being lightweight and corrosion-resistant. Its atomic mass is 26.98 amu, making its molar mass 26.98 g/mol. Suppose we need to find the mass of 3 moles of Al atoms. Using the molar mass calculation formula: \[\text{Mass of Al} = 3 \text{ mol} \times 26.98 \text{ g/mol} = 80.94 \text{ g}\]This means 3 moles of Al atoms weigh 80.94 grams. Calculations like these are useful in chemistry to quantify substances in reactions.
Chlorine (Cl) Atoms
Chlorine (Cl) is a highly reactive greenish-yellow gas in its pure form. Its atomic mass is 35.45 amu, translating to a molar mass of 35.45 g/mol. To find the mass of 2 moles of Cl atoms, use the formula: \[\text{Mass of Cl} = 2 \text{ mol} \times 35.45 \text{ g/mol} = 70.90 \text{ g}\]Thus, 2 moles of Cl atoms weigh 70.90 grams. Understanding these calculations helps in preparing chemical solutions and predicting the results of reactions.

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Most popular questions from this chapter

Fluorine is so reactive that it forms compounds with several of the noble gases. (a) When \(0.327 \mathrm{~g}\) of platinum is heated in fluorine, \(0.519 \mathrm{~g}\) of a dark red, volatile solid forms. What is its empirical formula? (b) When \(0.265 \mathrm{~g}\) of this red solid reacts with excess xenon gas, \(0.378 \mathrm{~g}\) of an orange-yellow solid forms. What is the empirical formula of this compound, the first to contain a noble gas? (c) Fluorides of xenon can be formed by direct reaction of the elements at high pressure and temperature. Under conditions that produce only the tetra- and hexafluorides, \(1.85 \times 10^{-4} \mathrm{~mol}\) of xenon reacted with \(5.00 \times 10^{-4} \mathrm{~mol}\) of fluorine, and \(9.00 \times 10^{-6} \mathrm{~mol}\) of xenon was found in excess. What are the mass percents of each xenon fluoride in the product mixture?

Serotonin \((\mathscr{M}=176 \mathrm{~g} / \mathrm{mol})\) transmits nerve impulses between neurons. It contains \(68.2 \%\) C, \(6.86 \%\) H, \(15.9 \%\) N, and \(9.08 \%\) O by mass. What is its molecular formula?

Elemental phosphorus occurs as tetratomic molecules, \(\mathrm{P}_{4}\). What mass (g) of chlorine gas is needed to react completely with \(455 \mathrm{~g}\) of phosphorus to form phosphorus pentachloride?

What is the molecular formula of each compound? (a) Empirical formula \(\mathrm{CH}_{2}(\mathscr{A}=42.08 \mathrm{~g} / \mathrm{mol})\) (b) Empirical formula \(\mathrm{NH}_{2}(\mathscr{M}=32.05 \mathrm{~g} / \mathrm{mol})\) (c) Empirical formula \(\mathrm{NO}_{2}(\mathscr{M}=92.02 \mathrm{~g} / \mathrm{mol})\) (d) Empirical formula CHN \((\mathscr{M}=135.14 \mathrm{~g} / \mathrm{mol})\)

In the following reaction, \(2.35 \mathrm{~mol}\) of \(\mathrm{NH}_{3}\) reacts with \(2.75 \mathrm{~mol}\) of \(\mathrm{O}_{2}\); how many moles of water form? $$ 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) $$
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