Solutions, States of Matter, and Thermochemistry - College Chemistry

Most salts containing halogens are soluble. Carbonates, phosphates, sulfides, oxides, and hydroxides are insoluble except for cations containing alkaline earth metals and hydroxides of calcium, strontium, and barium, which are slightly soluble.

Start by writing the equation for the dissolution of calcium hydroxide.

Next, set up the following table to show the equilibrium concentrations of the ions:

| | \[ \] | \[\] | | | -------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------- | ---- | | Initial | 0.00 | 0.00 | | Change | +S | +2S | | Equilibrium | S | 2S |

Now substitute in the values of the concentrations of the ions into the expression to find .

Now, plug in the given value and solve for , the molar solubility.

For this question, we're told that an aqueous solution of magnesium fluoride is saturated. We're then told that the fluoride concentration in the solution is reduced by a factor of two, and we're asked to find how the magnesium concentration would need to change in order to keep the solution saturated.

First, it's important to recall what saturation means. Some substances cannot dissolve in water, whereas others can dissolve readily. In other words, different substances will dissolve to differing degrees in water. The dissolution of a compound in a solvent such as water can be represented by an equilibrium expression. When there is a relatively small amount of solute added, the solution is said to be unsaturated. This means that all of the added solute will dissolve. As more and more solute is added to the water, there will eventually reach a point at which so much solute is present that it can no longer dissolve. When this happens, any additional solute will not dissolve and will instead form a precipitate in the solution. This condition is referred to as supersaturated. Saturation is the "sweet spot" so to speak; it is the point in between unsaturated and supersaturated where the maximum amount of solute has been added to the solution where all of the solute can be in the dissolved form. In other words, saturation refers to the maximum concentration of added solute where there is NO precipitation.

In order to set up an equilibrium expression, we can first write out the reaction in which magnesium fluoride dissolves.

Knowing the reaction, we can now write an equilibrium expression. Remember that pure solids and liquids don't appear in equilibrium expressions! Thus, this expression will only contain the products of the above reaction.

In the above expression, refers to the solubility product constant, which is just a quantitative way of expressing the degree to which a given compound can dissolve within a given solvent.

Since the equilibrium expression tells us the concentrations necessary to have a saturated solution, we can determine how a change in fluoride concentration would affect the equilibrium. Then, we can determine what changes to magnesium are needed.

If the fluoride concentration were to be cut in half, the value would be decreased by a factor of . This means that in order to maintain the value, we would have to increase the magnesium concentration by a factor of in order to compensate for the loss of fluoride.

A closed system allows for the exchange of energy between the system and its surroundings, but does not allow the exchange of matter. This is the definition of a closed system. An open system allows for the exchange of both matter and energy between the system and its surroundings. An isolated system on the other hand does not allow the exchange of either matter or energy between the system and its surroundings.

Recall the following equation:

Now, since the bomb calorimeter keeps the volume constant, we know the following relationship:

Thus, we can then write the following equation for :

Start by finding :

From this, we know that

Now, find .

Your answer must have significant figures.

In this question, we're given the mass of copper, along with its specific heat capacity, and we're asked to determine the amount of heat energy necessary to increase its temperature by a given amount.

To solve this problem, we'll need to make use of the following equation.

Since we know what the values are for the mass and specific heat, we'll need to figure out what the temperature will be. Since the Kelvin and Celsius temperature scales both change by the same amount and only differ at their zero point, we can take the difference of the temperatures in degrees Celsius and use that value (since it will be equivalent to the change in the Kelvin temperature as well).

Plugging this information into the first expression, we can solve for the amount of heat energy that will bring this mass of copper to the desired temperature.

In this question, we're asked to identify an answer choice that would be expected to give us a solution with the greatest osmotic pressure. Remember that osmotic pressure is proportional to the total number of dissolved solute particles in solution, regardless of the identity of those solute particles.

When looking at the answer choices, we need to keep in mind two things. First, we need to recognize the numerical value given for the concentration of the compound given. Secondly, we need to identify if the compound shown is capable of dissociating in solution to give rise to even more solute particles. This is important, as it would affect the osmotic pressure.

would be expected to have the largest osmotic pressure because, in total, this would be a solution after dissociation occurs.

Colligative properties are properties of solutions which depend on the number of dissolved particles in solution. The four main colligative properties are:

1. Freezing point depression: The presence of a solute lowers the freezing point of a solution as compared to that of the pure solvent.

2. Boiling point elevation: The presence of a solute increases the boiling point of a solution as compared to that of the pure solvent.

3. Vapor pressure depression: The vapor pressure of a pure solvent is greater than that of a solution containing a non-volatile liquid. The lowering of vapor pressure leads to boiling point elevation.

4. Osmotic pressure: The osmotic pressure of a solution is the pressure difference between the solution and pure solvent when the two are in equilibrium across a semipermeable membrane. Because it depends on the concentration of solute particles in solution, it is a colligative property.

Electronegativity is not a property of solutions reliant on the number of dissolved particles, but a property of atoms themselves.

This question is asking us to identify a solution that increases the boiling point of water by the greatest amount.

To answer this, we need to understand the concept of colligative properties. When a solute dissolves in a solvent such as water, various physical properties are affected. The four colligative properties that change as a result of the addition of solute are freezing point, boiling point, vapor pressure, and osmotic pressure.

With regards to boiling point, as more solute is added to a solution, the boiling point increases. This is due to the fact that addition of solute makes it more difficult for the solute molecules to gain enough kinetic energy at the solution's surface to escape as a gas.

Furthermore, the identity of the solute does not matter. Thus, we need to look only at the number of dissolved solute particles rather than their identity. A compound such as sucrose will not dissociate in solution, which means that the osmotic pressure of the solution is the same as the concentration of sucrose.

Compounds that can dissociate into two or more particles will increase the osmolarity of the solution further. In this case, will double the stated osmolarity. , on the other hand, will dissociate completely because it is a strong acid, however the protons will not contribute to the osmolarity.

is able to dissociate into three equivalents of particles in solution. Thus, its initial concentration will be tripled, which gives it the highest osmolarity of any of the choices shown and will thus increase the boiling point by the greatest amount.

This equation explicitly shows how the rate of effusion is inversely proportional to the molar mass of a gas in a gaseous solution.

Because , time relates to molar mass by:

Simplifying this equation, we see that:

As a result, time relates directly to molar mass

Recall Graham's Law of Effusion for two gases, A and B:

From the equation, we know the following:

Thus, we can solve for the molar mass of the unknown gas. Let be the molar mass of the unknown gas.

Make sure that your answer has significant figures.

We're being asked to compare the effusion rates of oxygen and carbon dioxide.

Remember that effusion is the spontaneous movement of a gas through a small hole from one area to another. It's worth noting that at a given temperature, the average speed of all gas molecules in a system is used to calculate the average kinetic energy of the gas particles. This dependence of kinetic energy on temperature means that at a given temperature, any gas particle will have the same kinetic energy.

In this case, we can say that the kinetic energy of oxygen molecules in one system is equal to the kinetic energy of carbon dioxide molecules in another system. Furthermore, since mass is inversely proportional to velocity, identical kinetic energies would mean that as the mass of the gas particles in a system decreases, their velocity (and thus, effusion rates) would increase.

We can use this information to solve for the relative effusion rates between oxygen and carbon dioxide. By setting their kinetic energies equal to each other, we can derive an expression that relates their relative speeds to their relative masses.

Generally speaking, this expression shows how the velocity of any two gasses depends on their mass. In this case, the gasses are oxygen and carbon dioxide.

We can use the periodic table of the elements to find out the mass of each gas, and use that information to calculate the relative effusion rates.

This shows that oxygen will effuse at a rate that is about faster than carbon dioxide.

To solve this problem use Graham's Law of Effusion

By plugging in the values we can rewrite the equation as

For this question, we're given the relative effusion rates for two gasses. We're then told how the mass of each of these gasses is changed, and then we're asked to determine the new relative effusion rates of the two gasses.

First, we can recall the expression that describes the dependence of the effusion rates of two gasses on their mass. Since we're told that the rate of gas A is twice that of gas B, we can write the following expression.

Furthermore, since we're told that the mass of gas B is doubled and the mass of gas A is halved, we can determine how the rate will change.

Thus, we can see that the rate will change by a factor of two. Hence, the new rate will be . Thus, gas A will now effuse at a rate times that of gas B.

Thermal equilibrium: Thermal energy of the system is equal to thermal energy of the surroundings. Heat is defined as the energy transfer resulting from differences in thermal energy. Heat always flows from higher temperature to lower temperature. Heat transfer between a system and its surroundings stop when they reach thermal equilibrium, or when there is no difference in thermal energy. In this case, ice was dropped into the cup. Initially, the ice increases the temperature of the water, creating a cold glass with condensation. However, energy from the surroundings flow into the system (the glass of water) due to thermal difference and warm the glass of water until the two reach thermal equilibrium. At thermal equilibrium, there is no ice, no condensation, and the water temperature is room temperature.

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.

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.

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.

Since we are given the volume and the pressure of this sample of gas, we will need to use Boyle's Law, which states that the pressure and volume of a gas, at a constant temperature, are inversely related. As thus, we can then write the following equation:

Since all the answer choices are in units of atmospheres, we will need to convert the given units into atmospheres.

Plug in the given pressures and volume into the equation, and solve for .