List the following aqueous solutions in order of decreasing freezing point: \(0.040 \mathrm{~m}\) glycerin \(\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\right), 0.020 \mathrm{~m} \mathrm{KBr}\), \(0.030 \mathrm{~m}\) phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\)

First, we will identify the number of particles (ions or molecules) formed in water by each solute: 1. Glycerin (C3H8O3) - it is a molecular compound and will not form ions in water, so it forms 1 particle. 2. KBr - It is an ionic compound and will dissociate into 2 ions in water: K+ and Br-. 3. Phenol (C6H5OH) - it is a molecular compound and will not form ions in water, so it forms 1 particle.

Next, we will calculate the effective molality of particles for each solution by multiplying the molality of the solute (given in the exercise) by the number of particles formed by that solute in water: 1. \(0.040\ \mathrm{m}\) glycerin: \(0.040\ \mathrm{m} \times 1 = 0.040\ \mathrm{m}\) particles 2. \(0.020\ \mathrm{m}\) KBr: \(0.020\ \mathrm{m} \times 2 = 0.040\ \mathrm{m}\) particles 3. \(0.030\ \mathrm{m}\) phenol: \(0.030\ \mathrm{m} \times 1 = 0.030\ \mathrm{m}\) particles

We will now compare the effective molalities of particles to determine the order of decreasing freezing point: A higher effective molality of particles results in a larger freezing point depression, which in turn corresponds to a lower freezing point. Based on the effective molalities calculated in Step 2, we can order the solutions as follows: 1. \(0.040\ \mathrm{m}\) KBr - KBr has the highest effective molality of particles and will have the lowest freezing point. 2. \(0.040\ \mathrm{m}\) glycerin - Glycerin has the same effective molality as KBr but was originally less concentrated, so its freezing point is higher than KBr but lower than phenol. 3. \(0.030\ \mathrm{m}\) phenol - Phenol has the lowest effective molality of particles and will have the highest freezing point. Thus, the order of the solutions in decreasing freezing point is: KBr > Glycerin > Phenol