High School

A limestone building stone measures 51.7 cm long, 27 cm wide, and 15 cm thick. It is composed of 92% calcite, with the remaining volume being empty pore space.

1. What is the mass of this building stone in kg?
2. What would be its mass if it were marble? (Recrystallization of metamorphism eliminates the pore space. Assume the specific gravity (SG) of calcite is 2.7 g/cm³.)

- The mass of the limestone building stone is _____ kg.
- The mass of the building stone if it were marble is _____ kg.

Answer :

The mass of the building stone if it were marble, we need to consider that marble is a type of limestone that has undergone metamorphism, which eliminates the pore space. This means that the entire volume of the marble stone will contribute to its mass. We can follow the same steps as above, but using a SG marble value instead of SG calcite.

To calculate the mass of the limestone building stone, we need to determine its volume first. The volume of the stone can be calculated by multiplying its length, width, and thickness:

Volume = length x width x thickness = 51.7 cm x 27 cm x 15 cm

Next, we need to consider that the stone is 92% calcite and the rest is empty pore space. This means that only 92% of the calculated volume will contribute to the mass. The remaining 8% represents the empty pore space, which does not contribute to the mass. Therefore, we can calculate the effective volume of the stone:

Effective Volume = Volume x 0.92

Now, we can calculate the mass of the limestone building stone using its effective volume and the specific gravity (SG) of calcite. The specific gravity represents the density of a material relative to the density of water. In this case, we will assume SG calcite = 2.7 g/cm³:

Mass = Effective Volume x SG calcite

Finally, we can convert the mass from grams to kilograms:

Mass (kg) = Mass (g) / 1000

To calculate the mass of the building stone if it were marble, we need to consider that marble is a type of limestone that has undergone metamorphism, which eliminates the pore space. This means that the entire volume of the marble stone will contribute to its mass. We can follow the same steps as above, but using a SG marble value instead of SG calcite.Note: The specific gravity values for different types of marble can vary, but for simplicity, we will assume SG marble = 2.7 g/cm³.

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