Problem 107 - Chemistry and Chemical Reactivity

Question

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 \(\mathbf{C}\) (d) 7.4 mol \(\mathrm{Si}\) (e) 9.221 mol \(\mathrm{Na}\) (f) \(4.07 \times 10^{24}\) atoms Al (g) 9.2 mol \(\mathrm{Cl}_{2}\)

Step-by-Step Solution

Answer

The order is: H2, C, Al, Si, Na, Fe, Cl2.

Step 1: Determine Molar Mass

Calculate the molar mass for each element and molecule: - Fe (Iron): 55.85 g/mol - H2 (Hydrogen molecule): 2.02 g/mol - C (Carbon): 12.01 g/mol - Si (Silicon): 28.09 g/mol - Na (Sodium): 22.99 g/mol - Cl2 (Chlorine molecule): 70.90 g/mol - Al (Aluminum): 26.98 g/mol.

Step 2: Convert Atoms to Moles

Use Avogadro's number to convert the number of atoms to moles for Fe and Al:- Fe: \( \frac{3.79 \times 10^{24}}{6.022 \times 10^{23}} = 6.29 \text{ moles} \)- Al: \( \frac{4.07 \times 10^{24}}{6.022 \times 10^{23}} = 6.76 \text{ moles} \)

Step 3: Calculate the Mass for Each Element/Molecule

Calculate the mass using the formula: \( \text{mass} = \text{moles} \times \text{molar mass} \):- Fe: \( 6.29 \times 55.85 = 351.25 \text{ g} \)- H2: \( 19.921 \times 2.02 = 40.23 \text{ g} \)- C: \( 8.576 \times 12.01 = 102.97 \text{ g} \)- Si: \( 7.4 \times 28.09 = 207.87 \text{ g} \)- Na: \( 9.221 \times 22.99 = 212.15 \text{ g} \)- Cl2: \( 9.2 \times 70.90 = 652.28 \text{ g} \)- Al: \( 6.76 \times 26.98 = 182.38 \text{ g} \)

Step 4: Order the Masses from Smallest to Largest

List the masses in ascending order: 1. H2: 40.23 g 2. C: 102.97 g 3. Al: 182.38 g 4. Si: 207.87 g 5. Na: 212.15 g 6. Fe: 351.25 g 7. Cl2: 652.28 g

Key Concepts

Avogadro's Number

When dealing with atoms and molecules, chemists often need to convert between the number of atoms/molecules and moles. This is where Avogadro's number, which is approximately \(6.022 \times 10^{23}\), comes into play. A mole represents a quantity of \(6.022 \times 10^{23}\) items, be it atoms, molecules, or ions. Avogadro's number is particularly useful because it allows scientists to work with the macroscopic amounts of a substance. For example, if you're given \(3.79 \times 10^{24}\) atoms of iron (Fe), you can use Avogadro's number to convert this into moles.Here's the conversion:- For Iron (Fe):\[moles = \frac{3.79 \times 10^{24}}{6.022 \times 10^{23}} = 6.29 \text{ moles}\]This conversion is crucial because it simplifies further computations, such as calculating mass, where you need the amount in moles.

Molecular Mass Calculation

Understanding molecular mass is fundamental in chemistry. The molecular mass or molar mass of a substance is the mass of one mole of that substance, expressed in grams per mole (g/mol). This quantity helps chemists understand how much of a substance they are dealing with in a given chemical reaction or process.To find the molar mass, you usually sum up the atomic masses of the elements in a molecule, available on the periodic table:- Hydrogen ('\(\mathrm{H}_2\)'): Each \(\mathrm{H}\) atom has a mass of approximately 1.01 g/mol, so the molar mass of \(\mathrm{H}_2\) is \(2 \times 1.01 = 2.02\) g/mol.- Chlorine ('\(\mathrm{Cl}_2\)'): Each \(\mathrm{Cl}\) atom is about 35.45 g/mol, making \(\mathrm{Cl}_2\) 70.90 g/mol.By calculating molecular mass, you provide a foundation for converting moles to grams, which is necessary for implementing in practice the theoretical concepts of stoichiometry.

Mass Conversion in Chemistry

In chemistry, it is common to convert quantities between moles and grams. This process is crucial when you need to determine the mass of a substance involved in a chemical reaction.The formula for converting moles to grams is:\[\text{mass} = \text{moles} \times \text{molar mass}\]Let's see some examples to clarify:- For Sodium (Na), with a molar mass of 22.99 g/mol: If you have \(9.221\) moles, you calculate the mass as: \[ 9.221 \times 22.99 = 212.15 \text{ g} \] - For Silicon (Si), with a molar mass of 28.09 g/mol: If you have 7.4 moles, the calculation becomes: \[ 7.4 \times 28.09 = 207.87 \text{ g} \]This conversion is essential for balancing chemical equations, quantifying reactants, and calculating yields. Knowing how to convert mass and moles allows chemists to clearly articulate changes in matter.