Understanding One Degree of Water Hardness

Water hardness is typically measured in different units, often referred to as "degrees". There are several types of degrees, including English (Clark) degrees, French degrees, and German degrees. Hardness can also be expressed directly as concentration, commonly in milligrams per litre (mg/litre) or parts per million (ppm), usually as calcium carbonate ($\text{CaCO}_3$) equivalent.

The question asks for the equivalence of one degree of hardness in mg/litre. The options provided suggest a specific type of degree is being referred to, which corresponds to a particular numerical value in mg/litre.

Equivalence of One English Degree (Clark Degree)

One common unit for water hardness, particularly in some countries, is the English degree or Clark degree. This degree is defined based on the concentration of dissolved minerals in water.

By definition:

• One English degree of hardness is equivalent to 1 grain of calcium carbonate ($\text{CaCO}_3$) per Imperial gallon of water.

To convert this unit (grain/Imperial gallon) into milligrams per litre (mg/litre), we use standard conversion factors:

• 1 grain $\approx 64.8 \text{ milligrams (mg)}$
• 1 Imperial gallon $\approx 4.546 \text{ litres}$

Now, let's perform the conversion:

$\text{1 English degree} = \frac{\text{1 grain}}{\text{1 Imperial gallon}}$

Substitute the values in milligrams and litres:

$\text{1 English degree} = \frac{64.8 \text{ mg}}{4.546 \text{ litres}}$

Calculating the value:

$\text{1 English degree} \approx 14.25 \text{ mg/litre}$

Therefore, one English degree of hardness is approximately equivalent to 14.25 mg/litre (which is also equivalent to 14.25 ppm) when expressed as calcium carbonate equivalent.

This value aligns with one of the options provided, indicating that the question is referencing the English degree of hardness.

Let's look at how this compares to the given options in mg/litre:

• Option 1: 1425 mg/litre
• Option 2: 14.25 mg/litre
• Option 3: 142.5 mg/litre
• Option 4: 1.425 mg/litre

Based on our calculation, one English degree of hardness is approximately 14.25 mg/litre.

Understanding these different units is important when discussing water quality and treatment processes like softening, as hardness levels are often reported in these units.