Concept explainers
The oxide-to-metal volume (Pilling-Bedworth) ratios for the oxidation of the metals listed and comment whether oxides are protective or not.
Explanation of Solution
Write the formula for Pilling-Bedworth
In general, the Pilling-Bedworth ratios are determined for the 100 g mass of the metal.
Write the formula for volume from density.
The Pilling-Bedworth ratio alone will not predict the protective nature of the oxide film. The P.B. ratio is the additional factor to say that the metal’s oxide film is protective. The P.B. ration must be 1 or very close 1 to make the metal’s oxide film as a protective film.
Conclusion:
For Tungsten
The oxidation reaction tungsten is,
The molecular mass of the tungsten
The molecular mass of the tungsten oxide
Calculate the volume of the tungsten using equation (II).
The mass of
Calculate the volume of tungsten oxide
Calculate the Pilling-Bedworth ratio between tungsten and its oxide using equation (I).
Here, the P.B. ratio is
Thus, the tungsten oxide
For Sodium
The oxidation reaction sodium is,
The molecular mass of the sodium
The molecular mass of the sodium oxide
Calculate the volume of the sodium using equation (II).
The mass of
Calculate the volume of sodium oxide
Calculate the Pilling-Bedworth ratio between tungsten and its oxide using equation (I).
Here, the P.B. ratio is
Thus, the sodium oxide
Similarly, the Pilling-Bedworth ratios for the other metals listed in the given table is calculated and tabulated in below Table 1.
S. No. | Metal | P.B. ratio | Description |
1 | Tungsten, W | 2.01>1 | Non protective |
2 | Sodium, Na | 0.57<1 | Non protective |
3 | Halnium, Hf | 1.62>1 | May protective |
4 | Copper, Cu | 1.74>1 | May protective |
5 | Manganese, Mn | 1.70>1 | May protective |
6 | Tin, Sn | 1.15>1, | Protective |
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Chapter 13 Solutions
Foundations of Materials Science and Engineering
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