---
title: "A metallurgist investigates the physical properties of two alloys derived from pure iron, \\(\\text{Fe}\\) (atomic radius \\(126\\text{ pm}\\), molar mass \\(55.85\\text{ g/mol}\\)):  – Alloy 1 is formed by introducing carbon, \\(\\text{C}\\) (atomic radius \\(77\\text{ pm}\\), molar mass \\(12.01\\text{ g/mol}\\)), which occupies interstitial sites within the \\(\\text{Fe}\\) crystal lattice with negligible change in unit cell volume. – Alloy 2 is formed by substituting \\(10\\%\\) of the lattice sites in pure \\(\\text{Fe}\\) with chromium atoms, \\(\\text{Cr}\\) (atomic radius \\(128\\text{ pm}\\), molar mass \\(52.00\\text{ g/mol}\\)).  Which of the following correctly predicts the densities of Alloy 1 and Alloy 2 relative to pure \\(\\text{Fe}\\), and provides the correct particulate justification for the malleability of Alloy 1 compared to pure \\(\\text{Fe}\\)?"
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date_modified: "2026-09-28T11:59:53+00:00"
---

# A metallurgist investigates the physical properties of two alloys derived from pure iron, \(\text{Fe}\) (atomic radius \(126\text{ pm}\), molar mass \(55.85\text{ g/mol}\)):

– Alloy 1 is formed by introducing carbon, \(\text{C}\) (atomic radius \(77\text{ pm}\), molar mass \(12.01\text{ g/mol}\)), which occupies interstitial sites within the \(\text{Fe}\) crystal lattice with negligible change in unit cell volume.
– Alloy 2 is formed by substituting \(10\%\) of the lattice sites in pure \(\text{Fe}\) with chromium atoms, \(\text{Cr}\) (atomic radius \(128\text{ pm}\), molar mass \(52.00\text{ g/mol}\)).

Which of the following correctly predicts the densities of Alloy 1 and Alloy 2 relative to pure \(\text{Fe}\), and provides the correct particulate justification for the malleability of Alloy 1 compared to pure \(\text{Fe}\)?

A metallurgist investigates the physical properties of two alloys derived from pure iron, \(\text{Fe}\) (atomic radius \(126\text{ pm}\), molar mass \(55.85\text{ g/mol}\)):

- Alloy 1 is formed by introducing carbon, \(\text{C}\) (atomic radius \(77\text{ pm}\), molar mass \(12.01\text{ g/mol}\)), which occupies interstitial sites within the \(\text{Fe}\) crystal lattice with negligible change in unit cell volume.
- Alloy 2 is formed by substituting \(10\%\) of the lattice sites in pure \(\text{Fe}\) with chromium atoms, \(\text{Cr}\) (atomic radius \(128\text{ pm}\), molar mass \(52.00\text{ g/mol}\)).

Which of the following correctly predicts the densities of Alloy 1 and Alloy 2 relative to pure \(\text{Fe}\), and provides the correct particulate justification for the malleability of Alloy 1 compared to pure \(\text{Fe}\)?

- **A.** Alloy 1 has a lower density than pure \(\text{Fe}\), Alloy 2 has a greater density than pure \(\text{Fe}\), and Alloy 1 is more malleable than pure \(\text{Fe}\) because the smaller \(\text{C}\) atoms facilitate the sliding of \(\text{Fe}\) atom planes.
- **B.** Alloy 1 has a greater density than pure \(\text{Fe}\), Alloy 2 has a greater density than pure \(\text{Fe}\), and Alloy 1 is less malleable than pure \(\text{Fe}\) because the \(\text{C}\) atoms increase the number of delocalized valence electrons in the lattice.
- **C.** Alloy 1 has a lower density than pure \(\text{Fe}\), Alloy 2 has a lower density than pure \(\text{Fe}\), and Alloy 1 is less malleable than pure \(\text{Fe}\) because the \(\text{C}\) atoms displace \(\text{Fe}\) atoms and generate vacant lattice positions.
- **D.** Alloy 1 has a greater density than pure \(\text{Fe}\), Alloy 2 has a lower density than pure \(\text{Fe}\), and Alloy 1 is less malleable than pure \(\text{Fe}\) because the interstitial \(\text{C}\) atoms hinder the layers of \(\text{Fe}\) atoms from sliding past one another.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123479/*