Calcite (CaCO3): bubbles strongly in cold acid
Magnesite (MgCO3): bubbles only in hot acid
Siderite (FeCO3): bubbles only in hot acid
Rhodochrosite (MnCO3): bubbles weakly in cold acid, strongly in hot acid
Smithsonite (ZnCO3): bubbles only in hot acid
Calcite is by far the most common in the calcite group, and is the only one that typically looks like our specimen. However, we know it isn't calcite. Sometimes magnesite occurs in white granular masses like our specimen, but the main suspect is dolomite (CaMg(CO3)2), which is not in the calcite family. It bubbles weakly in cold acid, strongly in hot acid. Because we're using weak vinegar, we will pulverize the specimen to make the reaction faster.

