For coagulation of 50 mL of a sol, 10 mL of 0.5M Cl$$^-$$ ion solution is required. What is the coagulating value of Cl$$^-$$ ion solution (Nearest integer)

The coagulating value is defined as the number of millimoles of electrolyte required to coagulate 1 liter of a sol.

Given:

• Volume of sol = 50 mL
• Volume of Cl⁻ ion solution used = 10 mL
• Concentration of Cl⁻ ion solution = 0.5 M

First, calculate the millimoles of Cl⁻ ions used:

Concentration = 0.5 M = 0.5 mol/L

Volume of Cl⁻ solution = 10 mL = 0.01 L

Moles of Cl⁻ = concentration × volume = $$0.5 \times 0.01 = 0.005$$ mol

Convert to millimoles: $$0.005 \times 1000 = 5$$ millimoles

Thus, 5 millimoles of Cl⁻ ions coagulate 50 mL of sol.

Now, find the millimoles required to coagulate 1 liter (1000 mL) of sol:

Using proportion:

$$\frac{5 \text{ millimoles}}{50 \text{ mL}} = \frac{x \text{ millimoles}}{1000 \text{ mL}}$$

Solve for $$x$$:

$$x = \frac{5 \times 1000}{50} = \frac{5000}{50} = 100$$ millimoles

Therefore, the coagulating value is 100 millimoles per liter.

The nearest integer is 100.