The ore which cannot be concentrated by froth floatation process is:

\(CaCO_3\)

The correct answer is option 1. \(CaCO_3\).

Let us delve deeper into the reasoning behind why certain ores can or cannot be concentrated by the froth flotation process.

Froth flotation is a method used primarily for the concentration of sulfide ores. In this process, the finely ground ore is mixed with water to form a slurry. Chemicals called collectors (e.g., pine oil, xanthates) are added, which selectively bind to the surface of the desired mineral particles, making them hydrophobic (water-repellent). Air is then bubbled through the slurry, and the hydrophobic particles attach to the air bubbles, rising to the surface as froth. This froth is skimmed off, and the concentrated ore is recovered.

Evaluation of Each Ore:

1. \(CaCO_3\) (Calcium Carbonate):

Type: Carbonate ore.

Calcium carbonate is not a sulfide ore but a carbonate ore. The froth flotation process is designed for sulfide ores and is not effective for carbonate ores like \(CaCO_3\). Carbonate ores are typically concentrated using methods like gravity separation or leaching.

Conclusion: Cannot be concentrated by froth flotation.

2. \(ZnS\) (Zinc Sulfide):

Type: Sulfide ore.

Zinc sulfide (sphalerite) is a classic example of a sulfide ore. It can be effectively concentrated by froth flotation because the zinc sulfide particles become hydrophobic when treated with appropriate chemicals, allowing them to be separated from the gangue.

Conclusion: Can be concentrated by froth flotation.

3. \(HgS\) (Mercury Sulfide, Cinnabar):

Type: Sulfide ore.

Mercury sulfide, also known as cinnabar, is a sulfide ore. Like other sulfide ores, it can be concentrated using the froth flotation process.

Conclusion: Can be concentrated by froth flotation.

4. \(Fe_2S\) (Iron Sulfide):

Type: Sulfide ore.

Iron sulfide (often as pyrite, FeS\(_2\)) is a sulfide mineral. Although the froth flotation process is sometimes used for concentrating iron sulfide ores, it is less common because the process is more selective for non-ferrous metal sulfides (like copper, lead, and zinc sulfides). However, technically, iron sulfide can be concentrated using this process.

Conclusion: Can be concentrated by froth flotation (though not typically used for iron sulfides).

Conclusion:

\(CaCO_3\) (Calcium carbonate) is not a sulfide ore and therefore cannot be concentrated by the froth flotation process. This method is mainly applicable to sulfide ores like \(ZnS\) and \(HgS\). Therefore, the correct answer is 1. \(CaCO_3\).