Question

By referring to Figure 13.18 , determine whether the addition of \(40.0 \mathrm{~g}\) of each of the following ionic solids to \(100 \mathrm{~g}\) of water at \(40^{\circ} \mathrm{C}\) will lead to a saturated solution: (a) \(\mathrm{NaNO}_{3},\) (b) KCl, (c) \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) (d) \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\)

Short answer

The addition of 40 g each of NaNO\(_3\), KCl, K\(_2\)Cr\(_2\)O\(_7\), and Pb(NO\(_3\))\(_2\) to 100 g of water at 40°C results in the following: (a) NaNO\(_3\): Not a saturated solution as the solubility (105 g) is greater than the 40 g added. (b) KCl: A saturated solution as the solubility at 40°C (40 g) is equal to the 40 g added. (c) K\(_2\)Cr\(_2\)O\(_7\): Not a saturated solution as the solubility (50 g) is greater than the 40 g added. (d) Pb(NO\(_3\))\(_2\): Not a saturated solution as the solubility (90 g) is greater than the 40 g added.

Step-by-step solution

Identify the solubility of compounds at 40°C

Refer to Figure 13.18 to determine the solubility of each ionic substance in g/100g of water at 40°C: (a) NaNO3: The solubility of NaNO3 at 40°C is approximately 105 g/100 g of water. (b) KCl: The solubility of KCl at 40°C is approximately 40 g/100 g of water. (c) K2Cr2O7: The solubility of K2Cr2O7 at 40°C is approximately 50 g/100 g of water. (d) Pb(NO3)2: The solubility of Pb(NO3)2 at 40°C is approximately 90 g/100 g of water. We now have the solubility of each compound at the given temperature.

Compare the solubility with the given mass

Now, we'll compare the solubility of each compound determined in Step 1 with the given mass of each ionic solid (40 g) to check if the addition of that solid to water will result in a saturated solution. (a) NaNO3: Since the solubility of NaNO3 at 40°C (105 g) is greater than the given mass of NaNO3 (40 g), the resulting solution will not be saturated. (b) KCl: The solubility of KCl at 40°C (40 g) is equal to the given mass of KCl (40 g), so the resulting solution will be saturated. (c) K2Cr2O7: Since the solubility of K2Cr2O7 at 40°C (50 g) is greater than the given mass of K2Cr2O7 (40 g), the resulting solution will not be saturated. (d) Pb(NO3)2: Since the solubility of Pb(NO3)2 at 40°C (90 g) is greater than the given mass of Pb(NO3)2 (40 g), the resulting solution will not be saturated.

Conclusion

By comparing the solubility of each compound at 40°C with the given mass, we conclude that: (a) The addition of 40 g NaNO3 to 100 g of water at 40°C will not lead to a saturated solution. (b) The addition of 40 g KCl to 100 g of water at 40°C will lead to a saturated solution. (c) The addition of 40 g K2Cr2O7 to 100 g of water at 40°C will not lead to a saturated solution. (d) The addition of 40 g Pb(NO3)2 to 100 g of water at 40°C will not lead to a saturated solution.

Key concepts

Saturated Solution

A saturated solution occurs when a solution contains the maximum amount of dissolved solute at a given temperature and pressure. Any additional solute will not dissolve and will remain as a separate phase, typically as solid particles at the bottom of the container.

In the given textbook exercise, the point at which a solution becomes saturated is critical. For example, when 40g of KCl is added to 100g of water at 40°C, it matches the solubility limit of KCl at this temperature; thus, the solution is exactly saturated. It's important to note that if you were to add more KCl beyond this point, it would not dissolve, indicating the solution has reached its carrying capacity for the solute.

Solubility Curves

Solubility curves are graphical representations that show how the solubility of substances changes with temperature. They are useful tools for understanding how much of a substance can be dissolved in a solvent at a specific temperature.

For students, interpreting solubility curves, like the one referenced in the exercise, i.e., Figure 13.18, is essential. It helps in predicting how much solute can be added before the solution becomes saturated. For instance, if the solubility of NaNO3 at 40°C is above the amount you want to dissolve, you can confidently add the solute knowing the solution will remain unsaturated.

Temperature Effect on Solubility

Temperature significantly affects the solubility of ionic compounds. In many cases, the solubility of a substance increases as the temperature rises, which is particularly true for most solid solutes.

However, this is not a universal rule – some substances have a solubility that decreases with increasing temperature. Understanding this concept helps in explaining why at 40°C, the solubility of substances like NaNO3 and K2Cr2O7 is higher than the 40g of solute we attempted to dissolve. Interestingly, for gases dissolved in liquids, increased temperature usually decreases solubility.

Ionic Solids in Water

Ionic solids, such as the compounds involved in the exercise, dissolve in water by dissociating into their constituent ions. This process is guided by the solubility product, which indicates the level at which a solute will dissolve to form a saturated solution.

Students need to understand that when ionic solids dissolve in water, they do so by interacting with water molecules that stabilize the ions. This process, called hydration, is crucial for substances like KCl and Pb(NO3)2. Furthermore, the solubility product helps us understand why adding 40g of various ionic compounds can lead to different outcomes in terms of saturation, based on their individual solubilities in water at a certain temperature.