The correct answer is 

First of all, we know this is an acid-base reaction.   is the reactant base and  is the reactant acid.  We know that these acid-base reactions create a water and a salt.  Also, we know that sulfates are soluble, except for those of calcium, strontium, and barium.  As a result,  is a precipitate in the reaction and water is produced.  

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:

 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.

The correct answer is .

 where  represents heat and  represents work.  

If a gas is expanding, it is doing work on the surroundings.  This means that  will be a negative value. Because the gas is absorbing heat,  entering the system and will be a positive value.  

Recall that the kinetic theory of gases states that if molecules are at the same temperature, then the mass of the molecules will determine their velocities. In a mixture of gases at a given temperature, the heavier gases will, on average, travel slower than the lighter ones. 

Thus, A must be the gas with the highest molar mass because it has the most molecules traveling at the slowest velocity.

There is more free space between gas particles than there is between liquid particles, and more free space between liquid particles than there is between solid particles. This makes gases very easy to compress as compared to solids and liquids.

Both liquids and gases can expand to fill their containers because the individual particles can move past each other. This is not possible in a solid because the individual particles are rigidly packed.

Additionally, the volume of a liquid or solid can increase by approximately eight hundred times when it becomes a gas. This large change in volume can be harnessed to do work. For example, a steam engine works when water boils to form a gas (steam), which has a larger volume. Steam can thus escape from the container in which it was produced and perform work.

Lastly, the pressure of a gas increases as more gas is added to the container. Pressure is defined as the force exerted by the gas over a certain area. If more gas particles are added to a fixed area, they will exert a greater force over that area, increasing the overall pressure.

Let's first look at the affects of adding an inert gas such as . He would not take part in the reaction, so the equation can be written as

Since He is on both sides of the equation, equilibrium is not affected.

Now let's look at the affects of heat. Because the reaction is exothermic, it can be rewritten as

Since heat is a product of the reaction, increasing temperature would shift the reaction to the left.

Finally, we know that changing the volume changes the internal pressure of the system. We know that the affect of this change is dependent on the number of moles in the gaseous phase. 

In order to increase the production of NH₃ (the side with the least number of moles), we need to increase the internal pressure of the system by decreasing the volume.

Decreasing the volume would increase the production of ammonia.

The pressure of the flask at  is .  

Because the volume between the flasks and the moles in each flask are constant, we can cancel out  and .

At STP, conditions are  and .  

Recall the van der Waals equation for non-ideal gases

Rewrite the equation using the known values and solve for P