Question

How does the number of molecules in a 1 g sample of P2 compare to the number of molecules in a 1 \(\mathrm{g}\) sample of \(\mathrm{P} 4\) ? The number of \(\mathrm{P} 2\) molecules is: F. less, because \(P 2\) has a larger AMM than does \(P 4\) . G. less, because \(P 2\) has a smaller AMM than does P4. H. greater, because \(P 2\) has a larger AMM than does P4. J. greater, because \(P 2\) has a smaller AMM than does P4.

Short answer

Explain your answer. Answer: In a 1 g sample, P2 has a greater number of molecules as compared to P4. This is because P2 has a smaller atomic molar mass (61.94 g/mol) compared to P4 (123.88 g/mol), which ultimately results in more moles of P2 and therefore a larger number of P2 molecules.

Step-by-step solution

Calculate the molar mass of P2 and P4

The molar mass of phosphorus (P) is 30.97 g/mol. Knowing that, we can calculate the molar mass of P2 and P4: Molar mass of P2 = 2 * (30.97 g/mol) = 61.94 g/mol Molar mass of P4 = 4 * (30.97 g/mol) = 123.88 g/mol

Finding the number of moles in each sample

To find the number of moles in a 1 g sample for both P2 and P4, use the following formula: Number of moles = (mass of sample)/(molar mass) Number of moles in 1 g of P2 = (1 g)/(61.94 g/mol) = 0.01615 mol Number of moles in 1 g of P4 = (1 g)/(123.88 g/mol) = 0.008077 mol

Calculate the number of molecules for P2 and P4

We will use Avogadro's number (6.022 x 10^23) to find the number of molecules in each 1 g sample. Number of P2 molecules = (0.01615 mol) * (6.022 x 10^23) ≈ 9.72 x 10^22 molecules Number of P4 molecules = (0.008077 mol) * (6.022 x 10^23) ≈ 4.86 x 10^22 molecules

Compare the number of molecules and choose the correct answer

Comparing the number of molecules, we find that the number of P2 molecules (9.72 x 10^22) is greater than the number of P4 molecules (4.86 x 10^22). We also observe that P2 has a smaller atomic molar mass as compared to P4 (61.94 g/mol < 123.88 g/mol). Hence, the correct answer is J. greater, because P2 has a smaller AMM than does P4.

Key concepts

Avogadro's number

Understanding Avogadro's number is crucial in chemistry, as it forms the foundation for mole-based calculations. Avogadro's number, often denoted as 6.022 x 10^23, represents the number of constituent particles (usually atoms or molecules) present in one mole of a substance.

In practice, this number allows chemists to equate mass in grams to the number of atoms or molecules in a sample—forming a bridge between the macroscopic scale of grams and the microscopic scale of molecules. For example, one mole of any element contains exactly Avogadro's number of atoms, and this fact is used to convert moles to molecules and vice versa, a transformation that features prominently in chemical stoichiometry.

Molar mass of molecules

The molar mass of molecules is the mass of one mole of a molecular substance. It's measured in grams per mole (g/mol), and it's the sum of the atomic weights of all the atoms in the molecule. Students can find atomic weights listed on the periodic table, and these weights reflect the average mass of all the isotopes of an element weighted by their respective natural abundances.

Calculating molar mass requires learners to multiply the atomic weight of each element in the molecule by the number of atoms of that element present, and then to sum these values. As an educational tool in chemistry education, it empowers students to tackle problems involving chemical quantities and reactant to product conversions.

Stoichiometry

The term stoichiometry is derived from the Greek words 'stoicheion' (element) and 'metron' (measure), and it relates to the calculation of the quantities of reactants and products in chemical reactions. Stoichiometry takes into account the conservation of mass where the total mass of reactants equals the total mass of products.

To understand stoichiometry, students must grasp the concepts of molar mass and Avogadro's number. These concepts help them understand how to balance chemical equations, calculate yields, and determine reagent quantities necessary for reactions. Simple exercises that ask students to predict the outcome of specific reaction amounts are common in chemistry education and are vital in building a solid foundation in the subject.

Chemistry education

Chemistry education emphasizes the need for a conceptual understanding of the subject's basics and offers a systematic approach to problem-solving. A solid grasp of the concepts like moles, molar masses, and stoichiometry form the basis for more complex studies in chemistry.

Educators often focus on exercises that encourage students to apply these concepts in real-world scenarios, which can also be an excellent way to engage with the material. Tools such as visual aids, interactive simulations, and hands-on lab work complement textbook exercises. These educational strategies help to cement the foundational knowledge that students need to excel in the field of chemistry.

Moles to molecules conversion

Conversion from moles to molecules is a fundamental skill in chemistry that involves using Avogadro's number. This conversion is crucial for students to quantify the number of discrete chemical entities in a given sample, whether dealing with individual molecules, formula units, ions, or other particles.

The process is straightforward: by multiplying the number of moles by Avogadro's number, students can determine the exact number of molecules present. This type of calculation is often presented in textbook exercises and is essential for lab work—where knowing the precise number of molecules involved in a reaction can dictate the success of an experiment.