In this question, we're told that a certain amount of a compound dissolved in water lowers the water's freezing point. We're asked to determine the molar mass of the compound.

First, we must recognize this as a freezing point depression problem. Recall that freezing point depression is one of the colligative properties associated with dissolving solute into a solvent such as water.

To begin, we need to use the equation for freezing point depression, which states that the change in freezing point is proportional to both the molality of the solution as well as the molal freezing point depression constant for the solvent in question (in this case, water).

The answer we have just calculated above is the molality, which is a different way of expressing concentration than molarity. Molality is expressed as the number of moles of solute per kilogram of solvent, whereas molarity is the number of moles of solute divided by the total volume of the solution.

The next thing we need to do is find out how many total moles of solute are present in the solvent water. To do this, we need to use the volume of water provided to us in the question, along with the density of water, to calculate the mass of water present. Together with the molality calculated above, this will allow us to know the total number of moles in solution.

Now that we know the total number of moles of solute (our compound) that exists in solution, we can use that information, together with the total mass of the compound given to us in the question stem, to calculate the compound's molar mass.

Recall that the heat gained by ice must be equal to the heat from the food.

Start by calculating the heat from the food by converting the Calories into joules.

Next, calculate the heat gained by the ice. Take this in three steps:

1. Heating the ice from  to 

2. Ice melting.

3. Raising the temperature of water from  to .

Set this value equal to the heat from the food and solve for the mass.

Convert to kilograms.

Remember that when any substance is undergoing a phase change, its temperature will remain constant. In other words, the energy being added is not increasing the average kinetic energy of any of the particles in the system.

Also, the internal energy will not remain constant. As heat energy is added, as in the question, the internal energy will necessarily increase. Even though the kinetic energy of the particles is not increasing, the potential energy is. This is because the intermolecular forces of attraction (mostly hydrogen bonds in this case) need to be broken apart. When energy is added, that raises the potential energy component of internal energy, despite the fact that kinetic energy (and thus, temperature) remains constant.

By definition, viscosity is the measure of a liquid's resistance to flow. If a liquid has a low viscosity, it has a low resistance to flow. It may not necessarily always have a low boiling point, melting point, and/or vapor pressure due to this characteristic. Viscosity is just a way to measure and describe one physical characteristic (resistance to flow) of a liquid. The volume of a liquid does not say anything about its physical properties.

Start by writing out the the chemical formulas for the reactants:

In order to figure out the possible products, combine the cation of one molecule with the anion of the other molecule.

For this reaction, the possible products are  and .

Next, use solubility rules to figure out if any precipitate is formed. Since compounds with are soluble,  is soluble. Since  is only soluble when paired with ,  is insoluble.

Thus, we can write the final chemical equation:

Recall the solubility rules:

 is generally soluble, except when paired with .

Solubility rules can help us find the answer to this question. 

First, solubility rules state that all compounds of Group 1A elements on the periodic table are soluble in aqueous solution. This means that all of the alkali metals, including potassium, form compounds which are soluble in aqueous solution; thus,  is soluble in aqueous solution.

Solubility rules also tell us that all ammonium salts (salts of ) are soluble. This means that  is soluble.

Next, solubility rules tell us that all bromide salts are soluble, except for those of , , and . Thus,  is not soluble in aqueous solution. However, as lithium is not included in that list,  is soluble in aqueous solution.

Remember the solubility rules for ionic solids in water:

1) Salts of group 1 (with few exceptions) and NH₄⁺ are soluble

2) Nitrates, acetates, and perchlorates are soluble

3) Salts of silver, lead, and mercury (I) are insoluble

4) Chlorides, iodides, and bromides are soluble

5) Carbonates, phosphates, sulfides, oxides, and hydroxides are insoluble. Exceptions: sulfides of group 2 cations and hydroxides of calcium, strontium, and barium are slightly soluble

6) Sulfates are soluble except for those of calcium, strontium, and barium

Following these rules, we see that MgOH is insoluble in water

Recall how to find the molality of a solution:

First, start by finding the moles of glucose that we have. The molar mass of glucose is .

Next, convert the grams of water into kilograms.

Now, plug in the moles of glucose and kilograms of water into the equation for molality.

Start by assuming that we have  of this solution. Recall that hydrogen peroxide has a molecular formula of .

Use the given density to find the mass of the solution.

Next, find the mass of the hydrogen peroxide present in the solution.

Convert the mass of hydrogen peroxide into moles of hydrogen peroxide.

Recall how to find the molarity of a solution:

Since we have  of solution, the molarity is .