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Lime is a crucial component of mortar, serving as a binder that helps to hold the other ingredients together. When mixed with sand and water, lime creates a paste that hardens over time, providing strength and durability to the mortar. This makes it essential in masonry work, where it's used for bonding bricks, stones, and blocks. Lime also contributes to the workability of the mortar, allowing for better manipulation and application during construction.

The other materials listed do not fulfill the primary role that lime plays in mortar composition. Calcium sulfate is primarily used in the formation of gypsum and is not a direct component of traditional mortar. Diatomaceous earth is often used as an absorbent or in filtration applications but does not contribute to the binding properties of mortar. Pea gravel is typically employed in concrete mixes for bulk and weight rather than in mortar, which generally relies on finer aggregates.