Question

Given a pair of elements and their mass relation, answer the following questions. (a) The mass of 4 atoms of \(\mathrm{A}=\) the mass of 6 atoms of B. Which element has the smaller molar mass? (b) The mass of 6 atoms of \(\mathrm{C}\) is less than the mass of 3 atoms of the element D. Which element has more atoms/gram? (c) Six atoms of E have a larger mass than six atoms of F. Which has more atoms/gram? (d) Six atoms of \(\mathrm{F}\) have the same mass as 8 atoms of \(\mathrm{G}\). Which has more atoms/mole?

Short answer

Additionally, identify the element with more atoms/gram in each of the following pairs: C or D, E or F, and the element with more atoms/mole in pair F or G. Answer: B has the smaller molar mass. C has more atoms/gram, F has more atoms/gram, and G has more atoms/mole.

Step-by-step solution

Set up the relationship for the mass ratio

Given the mass of 4 atoms of A is equal to the mass of 6 atoms of B, we can write the relationship as: \(4M_A = 6M_B\).

Solve for the molar mass ratio

Divide both sides of the equation by 4 and 6, respectively. We get: \(M_A = \dfrac{3}{2}M_B\).

Identify the element with the smaller molar mass

Since the molar mass of A is 1.5 times the molar mass of B, element B has the smaller molar mass. #b) Determining which element has more atoms/gram#

Set up the relationship for the mass ratio

Given the mass of 6 atoms of C is less than the mass of 3 atoms of D, we can write the relationship as: \(6M_C < 3M_D\).

Solve for the molar mass ratio

Divide both sides of the equation by 6 and 3, respectively. We get: \(M_C < \dfrac{1}{2}M_D\).

Identify the element with more atoms/gram

Since the molar mass of C is less than half the molar mass of D, element C has more atoms/gram. #c) Determining which element has more atoms/gram#

Set up the relationship for the mass ratio

Given the mass of 6 atoms of E is larger than the mass of 6 atoms of F, we can write the relationship as: \(6M_E > 6M_F\).

Solve for the molar mass ratio

Divide both sides of the equation by 6. We get: \(M_E > M_F\).

Identify the element with more atoms/gram

Since the molar mass of E is greater than the molar mass of F, element F has more atoms/gram. #d) Determining which element has more atoms/mole#

Set up the relationship for the mass ratio

Given the mass of 6 atoms of F is equal to the mass of 8 atoms of G, we can write the relationship as: \(6M_F = 8M_G\).

Solve for the molar mass ratio

Divide both sides of the equation by 6 and 8, respectively. We get: \(M_F = \dfrac{4}{3}M_G\).

Identify the element with more atoms/mole

Since the molar mass of F is \(\dfrac{4}{3}\) times the molar mass of G, element G has more atoms/mole.

Key concepts

Understanding Atomic Mass

Atomic mass is a fundamental concept in chemistry that refers to the mass of a single atom, usually expressed in atomic mass units (u). One atomic mass unit is defined as one-twelfth of the mass of a carbon-12 atom. Atomic mass takes into account the mass of both protons and neutrons in the atom's nucleus, as electrons contribute negligibly to an atom's overall mass. For instance, the atomic mass of hydrogen is approximately 1 u, and that of oxygen is approximately 16 u.

It's important to remember that atomic mass is not the same as molar mass, though they are numerically similar when expressed in grams per mole (g/mol). This numeric similarity arises because one mole of a substance is defined to contain exactly Avogadro's number of particles (approximately 6.022 x 10²³), whether they are atoms, molecules, ions, or other entities.

Atoms per Gram

The term 'atoms per gram' measures the number of atoms in one gram of an element. It is a way of expressing how densely packed atoms are within a given mass of material. To calculate atoms per gram, you divide Avogadro's number by the element's molar mass. Elements with a smaller molar mass will have more atoms per gram because there's a larger number of lighter atoms that can fit into a gram.

Closer examination of the relationship between mass and the number of atoms helps students to grasp why an element with a lower molar mass will yield more atoms per gram. This concept is crucial when comparing the density of atomic matter across different elements and has practical implications in topics such as stoichiometry, material science, and pharmaceutical dosing.

Atoms per Mole

Atoms per mole refers to the number of atoms contained in one mole of a substance. This figure is constant and is equal to Avogadro's number. For any substance, one mole contains the same number of entities as there are in 12 grams of carbon-12. This is incredibly useful in chemistry because it provides a bridge between the microscopic world of atoms and the macroscopic world of grams and kilograms.

When elements have different atomic masses, their moles have the same number of atoms, but those moles would have different masses. This distinction is essential in solving problems related to chemical reactions and quantitative analysis in chemistry. Also, in comparing different substances, understanding atoms per mole helps predict how specific amounts of various elements will behave in a reaction.

Chemical Elements Relationships

Chemical elements exhibit a variety of relationships based on their atomic structure and properties. The periodic table provides a framework that showcases these relationships, such as trends in atomic size, electronegativity, and ionization energy. Additionally, elements react and combine in fixed ratios to form compounds, abiding by the laws of stoichiometry.

One relationship of particular interest is the comparison of molar masses and their influence on substance behavior. For example, when comparing elements A and B in a given mass relation, the one with the smaller molar mass will have more atoms per mole and, consequently, potentially more reactivity in a given mass of the substance. It makes sense when you consider that there are more reactive particles within the same mass of a lighter substance than a heavier one. Understanding these kind of relationships is vital for grasping the principles of chemical reactions, predicting the outcomes of experimental procedures, and ultimately mastering the underlying concepts of chemistry.