A supersaturated solution of sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ is made by dissolving sucrose in hot water and slowly letting the solution cool to room temperature. After a long time, the excess sucrose crystallizes out of the solution. Indicate whether each of the following statements is true or false: (a) After the excess sucrose has crystallized out, the remaining solution is saturated. (b) After the excess sucrose has crystallized out, the system is now unstable and is not in equilibrium. (c) After the excess sucrose has crystallized out, the rate of sucrose molecules leaving the surface of the crystals to be hydrated by water is equal to the rate of sucrose molecules in water attaching to the surface of the crystals.

Step by step solution

01

(Statement (a) Analysis)

Let's analyze statement (a): "After the excess sucrose has crystallized out, the remaining solution is saturated". A saturated solution is one in which the maximum amount of solute has been dissolved in the solvent; if any more solute were to be added, it would not dissolve. After the excess sucrose crystallizes, the maximum amount of sucrose that can dissolve in the water at room temperature has been achieved. The remaining solution is indeed saturated. Therefore, statement (a) is true.

02

(Statement (b) Analysis)

Now, let's analyze statement (b): "After the excess sucrose has crystallized out, the system is now unstable and is not in equilibrium". A system at equilibrium is one in which the forward and reverse reactions are occurring at the same rate. In this case, after the excess sucrose has crystallized, there is no further change in the system unless external factors (like temperature or pressure) change again. At this point, the solution is saturated and the system is in equilibrium. Therefore, statement (b) is false.

03

(Statement (c) Analysis)

Finally, let's analyze statement (c): "After the excess sucrose has crystallized out, the rate of sucrose molecules leaving the surface of the crystals to be hydrated by water is equal to the rate of sucrose molecules in water attaching to the surface of the crystals". This statement is actually describing a system in equilibrium, where the rate of dissolution (sucrose molecules leaving the surface of the crystals and getting dissolved in water) is equal to the rate of crystallization (sucrose molecules in water attaching to the surface of the crystals). As explained earlier, at this point, the system is in equilibrium. Hence, statement (c) is true. In conclusion, the answers are: Statement (a): True Statement (b): False Statement (c): True

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