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Chapter 2: Problem 111

Put the following elements in order from smallest to largest mass: (a) \(3.79 \times 10^{24}\) atoms Fe (b) \(19.921 \mathrm{mol} \mathrm{H}_{2}\) (c) 8.576 mol \(\mathrm{C}\) (d) 7.4 mol \(\mathrm{Si}\) (e) 9.221 mol \(\mathrm{Na}\) (f) \(4.07 \times 10^{24}\) atoms \(\mathrm{Al}\) (g) 9.2 mol \(\mathrm{Cl}_{2}\)

Short Answer

Expert verified
\(\mathrm{H}_{2}\), C, Al, Si, Na, Fe, \(\mathrm{Cl}_{2}\) (smallest to largest mass).

Step by step solution

01

Convert Atoms to Moles

First, we need to convert the given number of atoms for Fe and Al to moles using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms per mole. For Fe, the moles are calculated as follows:\[\text{Moles of Fe} = \frac{3.79 \times 10^{24} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} \approx 6.297 \text{ moles}\]For Al, the moles are:\[ \text{Moles of Al} = \frac{4.07 \times 10^{24} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} \approx 6.762 \text{ moles}\]
02

Calculate Masses from Moles

Next, calculate the mass of each element or compound using the number of moles multiplied by the respective molar mass. The molar masses are: Fe is 55.85 g/mol, H鈧� is 2.02 g/mol, C is 12.01 g/mol, Si is 28.09 g/mol, Na is 22.99 g/mol, Al is 26.98 g/mol, and Cl鈧� is 70.90 g/mol.- \(\text{Mass of Fe} = 6.297 \text{ mol} \times 55.85 \text{ g/mol} = 351.68 \text{ g}\)- \(\text{Mass of } \mathrm{H}_{2} = 19.921 \text{ mol} \times 2.02 \text{ g/mol} = 40.21 \text{ g}\)- \(\text{Mass of C} = 8.576 \text{ mol} \times 12.01 \text{ g/mol} = 102.97 \text{ g}\)- \(\text{Mass of Si} = 7.4 \text{ mol} \times 28.09 \text{ g/mol} = 207.87 \text{ g}\)- \(\text{Mass of Na} = 9.221 \text{ mol} \times 22.99 \text{ g/mol} = 212.23 \text{ g}\)- \(\text{Mass of Al} = 6.762 \text{ mol} \times 26.98 \text{ g/mol} = 182.33 \text{ g}\)- \(\text{Mass of } \mathrm{Cl}_{2} = 9.2 \text{ mol} \times 70.90 \text{ g/mol} = 652.28 \text{ g}\)
03

Order from Smallest to Largest Mass

Now arrange the calculated masses in increasing order:1. \(\mathrm{H}_{2}\) - 40.21 g2. C - 102.97 g3. Al - 182.33 g4. Si - 207.87 g5. Na - 212.23 g6. Fe - 351.68 g7. \(\mathrm{Cl}_{2}\) - 652.28 g.Thus, the order from smallest to largest mass is: \(\mathrm{H}_{2}\), C, Al, Si, Na, Fe, \(\mathrm{Cl}_{2}\).

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Key Concepts

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

Molar Mass
When you hear about molar mass, think of it as the weight of one mole of a substance. It's often expressed in grams per mole (g/mol). Calculating molar mass involves adding up the atomic masses of each element in a compound. For instance, the molar mass of water (H鈧侽) is calculated by adding the molar masses of two hydrogen atoms and one oxygen atom. Hydrogen's molar mass is approximately 1.01 g/mol, and oxygen鈥檚 is around 16.00 g/mol. Hence, water's molar mass sums up to about 18.02 g/mol. Knowing the molar mass is crucial because it lets you convert between the mass of a substance and the amount in moles, which is essential for stoichiometry. Whether you're converting from grams to moles or vice versa, molar mass acts as the bridge connecting mass to amount.
Avogadro's Number
Avogadro鈥檚 number is a fundamental constant used in chemistry. It acts as a key that unlocks the connection between the macroscopic and microscopic worlds. This number, approximately 6.022 x 10虏鲁, tells us how many atoms or molecules are in one mole of a substance. Think of it like counting grains of sand on a beach: just as unimaginable! Avogadro's number helps chemists convert between the number of individual atoms and the amount in moles. For example, if you have 1 mole of carbon atoms, you have 6.022 x 10虏鲁 carbon atoms. By using Avogadro's number, you can easily shift from counting particle scale to real-world amounts when calculating the composition of compounds or reactions.
Chemical Elements
Chemical elements are the primary building blocks of all matter. Each element has unique properties and can be found listed in the periodic table. The simplest form is a single atom, characterized by its atomic number 鈥� the number of protons in its nucleus. Elements are represented by symbols, like Fe for iron and He for helium. These symbols are universal, making communication easier across languages. Elements can combine to form compounds, like when hydrogen and oxygen form water. Knowing elemental properties is essential for understanding their behavior during reactions. They influence how elements interact, what compounds they form, and the reactions they undergo. This knowledge is fundamental for anyone studying chemistry, especially when predicting reaction outcomes or determining compound structures.
Mass Calculation
Calculating mass in chemistry is all about understanding relationships between moles, molar mass, and the number of particles. The following are key steps in mass calculation:
  • Convert particles (atoms, molecules) to moles using Avogadro's number if you're starting with a count of atoms or molecules.
  • Use the molar mass of the substance to convert between moles and grams. For example, if you know the number of moles of a substance, multiply it by the molar mass to get its mass in grams.
Understanding these conversions is crucial for stoichiometry, a branch of chemistry that uses quantitative relationships between substances in reactions. Accurately determining mass lets chemists predict yields, balance equations, and determine the proportions of elements in compounds. Mass calculation serves as the backbone for practical and theoretical chemistry tasks, bridging the gap between laboratory work and real-world applications.

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Most popular questions from this chapter

The structure of one of the bases in DNA, adenine, is shown here. Which represents the greater mass: \(40.0 \mathrm{g}\) of adenine or \(3.0 \times 10^{23}\) molecules of the compound?

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