Phases and Properties of Matter - Physical Chemistry

The dimensions of the cubic container are by by (cube has same length, height, and width); therefore, the volume of the cubic container is

Recall that is the same as ; therefore, the container can contain of volume. This means that all of the solid will fit into the container. Upon melting, the solid will expand and the volume will increase (as it becomes liquid). This means that the volume of the container will not be sufficient for the liquid and, consequently, lead to an overflow of the liquid.

Liquid is an intermediate phase, between solid and gas. Solids are characterized by tightly packed molecules in an organized manner whereas gases are characterized by greatly spread out molecules that are highly disordered; liquids lie somewhere in the middle. This means that they are more disordered than solids (more entropy) and less disordered than gases (less entropy).

The boiling point of a substance is always higher than the melting point; therefore, you always need higher energy to break the interactions between liquid molecules.

The key difference between a liquid and a gas is the distance between the molecules. Liquid molecules are closer together whereas gas molecules are spread apart. Intermolecular forces are the forces between adjacent molecules. Since they are highly spread apart, the gas molecules have lower intermolecular forces.

Hydrogen bonding occurs between water molecules. While intermolecular forces between molecules exist for most molecules, these forces are much weaker than the bond formed between a hydrogen from one molecule and an oxygen, fluorine, and/or nitrogen atom of another molecule. Since the molecules are held more tightly together, more energy is required to break those bonds. This results in a higher temperature required to boil water (boiling breaks bonds between molecules, and this causes the molecules to escape into the gas phase).

There are three main phases: solids, liquids, and gases. Solids molecules are closely packed in an organized, lattice structure, liquid molecules are more spread apart and more disorganized, and gas molecules are spread even farther apart from each other and are extremely disorganized. Each type of solid is made up of unique type of atoms. For example, magnesium metal is made up of magnesium atoms whereas copper metal is made up of copper atoms. Since they are made up of unique atoms, different types of solids have different interactions between atoms. Some have strong interactions whereas others have very weak interactions; therefore, the energy required to break these interaction and separate the atoms/molecules (melt) is different for each solid.

Recall that entropy is the level of disorder in a system. As mentioned, solids are highly organized structures; therefore, they will have the lowest entropy.

Freezing the is process of converting a liquid to a solid. This question is asking about the freezing process of liquid nitrogen to solid nitrogen; therefore, the end product of the reaction is solid nitrogen. Recall that solids are more tightly packed. This means that the volume taken up by the molecules in solid is lower than in liquid; therefore, solids generally have a lower volume. Mass, on the other hand, depends on the number of molecules present. Phase changes do not alter the amount of molecules present. For example, the end product in this question (solid nitrogen) will have the same amount of molecules as its liquid counterpart; therefore, the mass doesn’t change when the phase changes.

Density is defined as follows.

Since its volume decreases and the mass stays the same, a solid will have a lower density than liquid. Note that water is an exception to this general rule, as solid ice has a lower density (higher volume) than the same mass of liquid water. This is due to the arrangement of its hydrogen bonds throughout its crystalline structure.

Recall than an object floats on water if it has a lower density than water. A floating or submerged object in a liquid has a gravitational pull (downward force) equal to the buoyancy force (upward force). The force due to gravity (gravitational pull) depends only on the mass of the object. In this case, the object can never be submerged because the density of the solid cannot be changed (unless the phase of the object is changed). To submerge, the object has to be placed in a liquid with LOWER density.

The volume of fluid displaced depends on the volume occupied by the object in the liquid. When an object floats, only part of the object is inside the liquid. This means that only part of the object’s volume is occupied inside the liquid (lower volume of fluid displaced). If the object were to be submerged (in a different liquid), the entire volume of the object would be inside the liquid and there would be an increase in the volume of fluid displaced.

Viscosity is a measure of resistance to flow. A liquid with high viscosity is said to have strong forces between its layers, making it harder to flow whereas a liquid with low viscosity has weak forces between its layers, making it easier to flow. Viscosity is quantified by the coefficient of viscosity (higher the coefficient, higher the viscosity and higher the resistance to flow). The question states that fluid A has more trouble flowing; therefore, fluid A has higher coefficient of viscosity and stronger forces between layers.

Poiseuille’s principle quantifies the flow rate of a fluid through a pipe to numerous variables as follows.

where is the flow rate, is change in pressure, is radius, is viscosity, and is length. We can see that viscosity and length terms are in the denominator; therefore, flow rate and these two terms are inversely related. This means that increasing viscosity and/or length of pipe will decrease the flow rate (and vice versa). Note that the radius has the biggest exponential factor; therefore, altering radius of the pipe will contribute to the biggest change in flow rate.

To solve this question, we need to use the continuity equation and Bernoulli’s equation. The continuity equation is as follows:

where is flow rate, is velocity, and is the area. This equation states that that the flow rate of a fluid is the same, regardless of changes in velocity and area. The equation implies that as the area is increased (for example, ) the velocity () decreases to maintain a constant flow rate and vice versa. The question states that End A has the larger radius; therefore, the velocity is lower at End A.

Bernoulli’s equation is as follows

where is pressure, is density, is velocity, is acceleration due to gravity, and is the height from ground. This equation implies that as velocity is increased on one side, the pressure decreases to compensate. Since we already determined that End B has the higher velocity, it will also have the lower pressure.

The argon gas, as the problem states, is under constant temperature with varying volume and pressure, so we need to use Boyle's Law:

We are given the initial pressure, the initial volume, and the final pressure, and need to solve for the final volume. Therefore, we can rearrange Boyle's law to be as follows:

Plug in known values and solve.

The methane gas, as the problem states, is under constant temperature with varying volume and pressure, so we need to use Boyle's Law:

We are given the initial pressure, the initial volume, and the final volume and need to solve for the final pressure. Therefore, we can rearrange Boyle's law to be as follows:

Plug in known values and solve.

There are three main gas laws. Avogadro’s law states that the moles of a gas is directly proportional to the volume (under constant pressure and temperature). Boyle’s law states that the pressure of the gas is inversely proportional to the volume (under constant moles and temperature). This means that the pressure decreases proportionally when the volume increases. Charles’ law states that the temperature is directly proportional to the volume (under constant moles and pressure). The question states that the piston moves up. This means that the volume of the gas is expanding inside and pushing the piston up to make room for the expanding gas. The gas expansion occurs due to increased temperature (Charles’ law).

To solve this question we need to use the ideal gas law equation:

Above, is pressure in , is volume in liters, is moles, is , and is temperature in Kelvins. The question gives us pressure, volume, and temperature; therefore, we can solve for . First, we need to convert temperature from Celsius to Kelvins.

Rearrange the ideal gas law and solve for :

The question states that you place one gram of gas in the container. Since we know the moles, we can solve for the molecular weight of the gas and figure out its identity from the molecular weight.

The molecular weight of oxygen gas, is ; therefore, the unknown gas must be oxygen.

First, we need to figure out which gas law is applicable here. The question states that temperature and moles are constant. This means that we are dealing with Boyle’s law, which states that pressure is inversely proportional to volume. Inversely proportional means that the pressure decreases as volume increases and vice versa. Note that the relationship is still linear (change in one variable causes a proportional change in the other variable), but the two variables have a negative correlation. Positive correlation means increasing or decreasing a variable would also increase or decrease the other variable, respectively.

Recall that Charles’ law defines the relationship between temperature and volume at constant pressure and constant moles. The law states that the two variables are directly proportional to each other. This means that increasing or decreasing temperature will have the same effect on volume. This makes sense because increasing the temperature increases the kinetic energy of the particles. This makes it easier for particles to move away from each other and expand, which results in an increase in volume.

Condition I is true. Pressure and volume are inversely proportional. The ideal gas law with volume can be rederived to show this:

We introduce an expression for moles:

Where is moles, is mass, and is molar mass in

Rearranging (1) to solve for and plugging into the following:

We get:

(2)

Finally, we use the following for density, where is volume, and plug into (2)

The masses cancel out and we have the ideal gas law expressed with volume and moles.

Condition II is false. It is clear from the equation that pressure and density are directly proportional.

Condition III is true because it is clear from the equation that temperature and pressure are directly proportional.

Condition IV is true because density and temperature are on the same side of the equation in the numerator, so the must be inversely proportional.

Condition V is false because the ideal gas constant and molar mass can be rearranged to be on opposite sides of the equation and in the numerator.

Gases deviate from ideal conditions at low temperature and high pressure. This because the postulates of the kinetic molecular theory of gasses ignore the volume of the molecules and all interactions between gas molecules. However, neither are true for real gasses. As the temperature increases, the kinetic energy of the particles can overcome the intermolecular forces of attraction or repulsion between the molecules. At high pressures, and subsequently low volume, the distance between molecules becomes shorter, and therefore intermolecular forces become significant. So, ideal conditions are when the distance between molecules is great, and the energy each molecule has is much greater in relative magnitude to the intermolecular forces. This occurs when the pressure is low, and the temperature is high.

All the statements say similar things, but only one correctly identifies the resulting change to volume and pressure. Let's break things down by the correction.

Correction 1:

The correction decreases the volume, since it is subtracting from the overall volume. As n (or the number of molecules) goes up, volume will go down.

Correction 2:

Since we are subtracting from the overall pressure, we are correcting for molecular attraction by decreasing pressure. We are doing this with a term that gets largerwhen increases and and gets larger as decreases.

Generally speaking, carbonate salts are insoluble, unless the carbonate is paired with an alkali metal. Magnesium carbonate, as a result, is considered an insoluble salt.

Salts containing alkali metals, ammonium, or nitrate ions are considered soluble. Phosphates, on the other hand, are generally considered insoluble, unless paired with an alkali metal or ammonium ion.