Question

Calculate the Pilling-Bedworth ratio when Fe oxides to FeO. The atomic weight of Fe is 55.8 gm, the atomic weight of Oxygen is 16 gm, density of Fe is 7.87 gm/cc and density of FeO is 5.70 gm/cc

• A. 0.777
• B. 3.777
• C. 2.777
• D. 1.777

Hint:

A Pilling-Bedworth ratio greater than 1 indicates a protective oxide layer, while a ratio less than 1 suggests the oxide may not provide protection.

Answer 1

The Correct Option is D

The Pilling-Bedworth ratio (PBR) is calculated using the formula:

\[ \text{PBR} = \frac{\text{Volume of oxide produced}}{\text{Volume of metal consumed}} \]

To find the volume of oxide produced, we use the formula for the volume of a substance:

\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

Step 1: Calculate the volume of Fe (metal consumed):

\[ \text{Volume of Fe} = \frac{\text{Atomic weight of Fe}}{\text{Density of Fe}} = \frac{55.8}{7.87} = 7.09 \, \text{cm}^3 \]

Step 2: Calculate the volume of FeO (oxide produced):

\[ \text{Volume of FeO} = \frac{\text{Atomic weight of Fe} + \text{Atomic weight of O}}{\text{Density of FeO}} = \frac{55.8 + 16}{5.70} = \frac{71.8}{5.70} = 12.61 \, \text{cm}^3 \]

Step 3: Now calculate the Pilling-Bedworth ratio:

\[ \text{PBR} = \frac{12.61}{7.09} \approx 1.777 \]

, So, the correct answer is option (D).