Animated Solution for Chemistry - Surface Chemistry: 100 mL of $0.0018\%\text{ (w/v)}$ solution of ${\text{Cl}}^{-}$ ion was the minimum concentration of ${\text{Cl}}^{-}$ required to precipitate a negative sol in one h. The coagulating value of ${\text{Cl}}^{-}$ ion is ......... (Nearest integer)

When dealing with colloidal solutions, stability is everything. But what happens when we want to break that stability and force the particles to clump together? We introduce an electrolyte. The coagulation value (or flocculation value) is the precise metric we use to measure the power of an electrolyte.

By standard IUPAC definition, the coagulation value is the minimum concentration of an electrolyte required to completely coagulate $1\text{ L}$ of a colloidal sol. Crucially, this concentration must be expressed in millimoles per litre (mmol/L). This specific unit is the trap where most students stumble.

In our problem, we are given a $0.0018\%\text{ (w/v)}$ solution of ${\text{Cl}}^{-}$ ions. Let's break down what this percentage actually means in physical terms.

The term $\%\text{ (w/v)}$ stands for weight by volume. It tells us the mass of the solute in grams present in exactly $100\text{ mL}$ of the solution. Therefore, a $0.0018\%\text{ (w/v)}$ solution implies that there are $0.0018\text{ g}$ of ${\text{Cl}}^{-}$ ions floating around in every $100\text{ mL}$ of the mixture.

Remember our definition? Coagulation value is strictly defined for $1\text{ L}$ (which is $1000\text{ mL}$) of the solution. Our current data is only for $100\text{ mL}$.

To find the mass of ${\text{Cl}}^{-}$ in a full litre, we simply scale up our values by a factor of $10$.

Now we know that there are $0.018\text{ g}$ of ${\text{Cl}}^{-}$ ions in $1\text{ L}$ of the solution.

We have the mass, but the coagulation value demands millimoles. Let's bridge that gap. First, we convert the mass into moles by dividing it by the molar mass of a chloride ion, which is $35.5\text{ g/mol}$.

To convert these moles into millimoles, we multiply the entire expression by $1000$.

All that is left is the final arithmetic. Dividing $18$ by $35.5$ gives us approximately $0.507\text{ mmol/L}$.

The question specifically asks for the answer rounded to the nearest integer. Since the first decimal digit is $5$, standard rounding rules dictate that we round up to the next whole number.

And there we have it! By carefully following the units and the definition, we arrive at the perfect integer answer.