Question

One gram of \(\mathrm{PbCl}_{2}\) is dissolved in \(1.0 \mathrm{~L}\) of hot water. When the solution is cooled to \(25^{\circ} \mathrm{C}\), will some of the \(\mathrm{PbCl}_{2}\) crystallize out? If so, how much?

Short answer

If so, how much will crystallize out? Answer: Yes, 0.90 grams of PbCl₂ will crystallize out when the solution is cooled to 25°C.

Step-by-step solution

Find the solubility of PbCl₂ at 25°C

To determine if PbCl₂ will crystallize out, we need to know its solubility at 25°C. Look up the solubility of PbCl₂ at 25°C in a reference source or online. The solubility of PbCl₂ at 25°C is 0.010 g/100mL.

Calculate the concentration of the solution after dissolving

Convert the solubility from grams per 100 mL to grams per liter (L) by multiplying by 10. Then, divide the mass of the dissolved PbCl₂ by the volume of the solution to find the concentration of the solution in g/L. Solubility at 25°C = 0.010 g/100 mL * 10 = 0.10 g/L Concentration of solution = (1 g) / (1.0 L) = 1.0 g/L

Determine if PbCl₂ will crystallize out

Compare the concentration of the solution (1.0 g/L) to the solubility of PbCl₂ at 25°C (0.10 g/L). If the concentration is greater than the solubility, then PbCl₂ will crystallize out. 1.0 g/L > 0.10 g/L, so PbCl₂ will crystallize out.

Calculate the amount of PbCl₂ that will crystallize out

To find the amount of PbCl₂ that will crystallize out, subtract the solubility at 25°C from the concentration of the solution and multiply it by the volume of the solution. Amount of PbCl₂ = (1.0 g/L - 0.10 g/L) * 1.0 L = 0.90 g So, 0.90 grams of PbCl₂ will crystallize out when the solution is cooled to 25°C.