How is a hardness of 100 mg/L expressed as CaCO3 in grains per gallon?

To convert hardness from milligrams per liter (mg/L) expressed as calcium carbonate (CaCO3) to grains per gallon (gpg), a specific conversion factor is applied. The conversion involves several steps, beginning with understanding the relationships between the units.

First, it's important to recognize that 1 grain per gallon is equivalent to approximately 17.1 mg/L. This means to convert from mg/L to grains per gallon, you can divide the hardness value in mg/L by this conversion factor.

In this case, you take 100 mg/L of hardness expressed as CaCO3:

1. Convert mg/L to grains per gallon:

[ 100 , \text{mg/L} \div 17.1 , \text{mg/L per gpg} \approx 5.85 , \text{gpg} ]

Therefore, the hardness of 100 mg/L as CaCO3 translates to approximately 5.85 grains per gallon. This aligns perfectly with the correct answer, highlighting how precise unit conversions are crucial in water treatment calculations, particularly when changing from metric to imperial measurements used in various applications. Such conversions help in understanding the levels of hardness in water and informing treatment processes accordingly.