Question

Maximum number of molecules will be in (a) \(1 \mathrm{~g}\) of \(\mathrm{H}_{2}\) (b) \(10 \mathrm{~g}\) of \(\mathrm{H}_{2}\) (c) \(22 \mathrm{~g}\) of \(\mathrm{O}_{2}\) (d) \(44 \mathrm{~g}\) of \(\mathrm{CO}_{2}\)

Short answer

10 g of H₂ has the maximum number of molecules.

Step-by-step solution

Understand the Problem Statement

We need to determine which sample contains the maximum number of molecules. We have four different samples: (a) 1 g of H₂, (b) 10 g of H₂, (c) 22 g of O₂, and (d) 44 g of CO₂.

Calculate Moles of H₂ in Option (a)

The molar mass of H₂ is approximately 2 g/mol. The number of moles of H₂ in 1 g is calculated as: \[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{1}{2} = 0.5 \text{ moles.} \]

Calculate Moles of H₂ in Option (b)

For 10 g of H₂, using the molar mass of 2 g/mol: \[ \text{Number of moles} = \frac{10}{2} = 5 \text{ moles.} \]

Calculate Moles of O₂ in Option (c)

The molar mass of O₂ is approximately 32 g/mol. Thus, the number of moles of O₂ in 22 g is: \[ \text{Number of moles} = \frac{22}{32} \approx 0.6875 \text{ moles.} \]

Calculate Moles of CO₂ in Option (d)

The molar mass of CO₂ is approximately 44 g/mol. The number of moles of CO₂ in 44 g is: \[ \text{Number of moles} = \frac{44}{44} = 1 \text{ mole.} \]

Compare Moles to Find Maximum

Now, compare all calculated moles: - Option (a): 0.5 moles - Option (b): 5 moles - Option (c): 0.6875 moles - Option (d): 1 mole. The maximum number of moles is in option (b) which is 5 moles.

Conclusion

Since the number of moles is directly proportional to the number of molecules (using Avogadro's number), the sample with the maximum number of moles has the maximum number of molecules. Option (b) has 5 moles, which means it has the maximum number of molecules.

Key concepts

Molar Mass

The concept of molar mass is fundamental when dealing with chemical substances. It represents the mass of one mole of a given substance, typically expressed in grams per mole (g/mol).
Molar mass is essential for converting between the mass of a substance and the number of moles it contains. To compute the molar mass, you sum up the atomic masses of all atoms in a molecule.

For instance, hydrogen molecule (H₂) has a molar mass of about 2 g/mol because each hydrogen atom has an atomic mass of approximately 1 g/mol. Similarly, the molar mass of an oxygen molecule (O₂) is roughly 32 g/mol, and carbon dioxide (CO₂) is about 44 g/mol.

• H₂: 1 g/mol (Hydrogen atom) × 2 = 2 g/mol
• O₂: 16 g/mol (Oxygen atom) × 2 = 32 g/mol
• CO₂: 12 g/mol (Carbon atom) + 16 g/mol (Oxygen atom) × 2 = 44 g/mol

Understanding molar mass allows you to calculate how many moles are present in a given mass of a substance, which is a crucial step in further calculations, such as determining the number of molecules using Avogadro's number.

Avogadro's Number

Avogadro's number is a key concept in chemistry, connecting microscopic atoms and molecules to the macroscopic amounts we can measure. It is defined as the number of particles (atoms, molecules, or ions) in one mole of a substance, and it is approximately equal to \(6.022 \times 10^{23}\).
This constant allows us to relate a substance's molar mass to the actual count of molecules present.

Whenever you calculate the number of moles from a given mass using the molar mass, Avogadro's number lets you convert those moles into the number of molecules. Hence, if we know the number of moles of hydrogen in a sample, we can multiply it by Avogadro's number to find out exactly how many molecules there are.

• 1 mole of H₂ contains \(6.022 \times 10^{23}\) molecules.
• This powerful conversion tool implies that in 5 moles of H₂, there are \(5 \times 6.022 \times 10^{23} = 3.011 \times 10^{24}\) molecules.

Avogadro's number bridges the gap between scale models and counting actual particles in chemical equations and reactions.

Stoichiometry

Stoichiometry is a section of chemistry that involves the calculation of reactants and products in chemical reactions. It requires a proportional understanding of the quantities of substances involved in reactions.
Using stoichiometry, you can predict how much of a product will form in a reaction when given amounts of reactants are used.

Stoichiometry uses ratios from balanced chemical equations to determine amounts. When given the mass of a substance, we use its molar mass to find moles, enabling us to apply mole ratios from the balanced chemical equation.

• For example, in calculating which sample contains the maximum number of molecules, understanding stoichiometry helps us convert between the mass and moles of each substance, using their molar masses.
• The balanced equation's mole ratios tell us about how substances will react substance in proportion to each other in a reaction, allowing calculation of the number of resulting molecules.

Whether you are determining the limiting reactant or calculating theoretical yields, stoichiometry is an indispensable tool for assessing and predicting chemical processes.