Question

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

Short answer

Answer: (a) B has a smaller molar mass, (b) D has more atoms per gram, (c) F has more atoms per gram, and (d) G has more atoms per mole.

Step-by-step solution

Identify the given information

We are given the mass relations of A and B as: \(4 \times \text{Mass of A} = 6 \times \text{Mass of B}\)

Find the molar mass ratio

We can find the molar mass ratio of A to B by dividing both sides of the equation by 4 and 6 (the respective number of atoms) respectively: \(\frac{\text{Mass of A}}{\text{Mass of B}} = \frac{6}{4}\) This simplifies to: \(\frac{\text{Mass of A}}{\text{Mass of B}} = \frac{3}{2}\)

Determine the element with the smaller molar mass

Since the ratio of the mass of A to B is \(\frac{3}{2}\), this means that A is more massive than B. Therefore, element B has a smaller molar mass. (b) The mass of 6 atoms of C is less than the mass of 3 atoms of the element D.

Identify the given information

We are given the inequality for the mass relations of C and D as: \(6 \times \text{Mass of C} < 3 \times \text{Mass of D}\)

Compare the mass ratio

Dividing both sides of the inequality by 6 and 3 (the respective number of atoms) respectively, we have: \(\frac{\text{Mass of C}}{\text{Mass of D}} < \frac{3}{6}\) This simplifies to: \(\frac{\text{Mass of C}}{\text{Mass of D}} < \frac{1}{2}\)

Determine which element has more atoms/gram

The inequality shows that the mass of C is less than half the mass of D. As the mass of a substance is directly related to its number of atoms, we can conclude that element D has more atoms per gram. (c) Six atoms of E have larger mass than six atoms of F.

Identify the given information

We are given the inequality for the mass relations of E and F as: \(6 \times \text{Mass of E} > 6 \times \text{Mass of F}\)

Compare the mass ratio

Dividing both sides of the inequality by 6 (the number of atoms), we have: \(\frac{\text{Mass of E}}{\text{Mass of F}} > 1\)

Determine which element has more atoms/gram

Since the mass of E is greater than the mass of F, we can conclude that element F has more atoms per gram. This is because a smaller mass per atom means there are more atoms in a fixed mass (or gram). (d) Six atoms of F have the same mass as 8 atoms of G.

Identify the given information

We are given the mass relations of F and G as: \(6 \times \text{Mass of F} = 8 \times \text{Mass of G}\)

Find the molar mass ratio

We can find the molar mass ratio of F to G by dividing both sides of the equation by 6 and 8 (the respective number of atoms) respectively: \(\frac{\text{Mass of F}}{\text{Mass of G}} = \frac{8}{6}\) This simplifies to: \(\frac{\text{Mass of F}}{\text{Mass of G}} = \frac{4}{3}\)

Determine which element has more atoms/mole

Since the ratio of the mass of F to G is \(\frac{4}{3}\), this means that F is more massive than G. Considering Avogadro's number, if an element has a smaller molar mass, it will have more atoms per mole. Therefore, element G has more atoms per mole.