Understand Freezing point/Melting point Part II : Freezing point/Melting Point Depression and Effect of Impurity

Melting point or freezing point depression  is basically the reduction of melting point or freezing point due to impurity.

The presence of impurity has two effects on melting and freezing point

1. lowers melting/freezing point ( If it is in range, it lowers end of range. For example, if the melting point is 188-189C, the mixture with impurity will be lower than 188C.

2. Melting point/freezing point will be in a range now instead of a sharp peak. For example, if the melting point were 188C, now it could be in a range of temperatures.

Why does this happen?

Adding impurity to the solution basically messes up the lattice (the structure of the molecule). This causes the structure of the molecule to break easily, meaning you need LESS temperature to melt it now. If it requires 180C to melt the solid, now it requires 100C. Pretty cool isnt it?

The opposite is true for freezing point

To form a structure of molecule from liquid, the correct lattice or structure is needed. Impurity basically impedes the formation of the correct structure due to difference in size, shape or charge. To allow the formation of solid to happen, you need lower entropy = low temperature. Therefore, when you add salt to water, it will remain as liquid at temperature at or below 0C, which is the freezing point of water.

Quoted from my previous post at this link

"Many people use salt to lower the freezing point of the ice. What does it mean? Imagine the temperature for today is 0 C. This is also the temperature when ice forms. Adding salt to the ice will lower it to -6 C. This means liquid will be frozen into solid at now -6 C (used to be 0 C). Since today's temperature is 0 C, the ice on the road after addition of salt is going to melt because we haven't reached -6 C (the new freezing point) yet. Until then, everything will be stayed at liquid."

This still remain true.

Understand the sign of work in electricity

Imagine the plates of a capacitor has a potential difference of 10V. How much work must be done in order to move the electron from the negative plate to positive plate?

Given that electric field goes from positive plate to negative plate. If you want to move the electron from negative to positive plate, you need to invest some energy to make that happen (positive work) because you are going up against the electric field.

The equation to solve that is W= qV. I was very confused about the sign of work due to the sign of V and q. However, I realize that no matter what you do, your work must be POSITIVE! Therefore, you can do whatever you want to q and V to make work positive :)

Understand how capacitor works

We all know that the purpose of capacitor is to store charges. But how does it work exactly?

Capacitor is made of two plates with non conducting material in between.

The top plate has positive charge (or negative) and the bottom plate has negative charge (or positive). Because of this, positive and negative charges both attract each other, keeping each other in place (so they wont go other places)--this is a form of storage.

Why do we need a non-conducting material in between? Well, if we have a conducting material in between instead, then the plates cannot hold charges, which destroys the purpose of the capacitor.

Understand the sign of work

At some point, we are all confused by the meaning of the sign of work; at least I did. 

Here is how I interpret the sign of work.

We all know that W=P times change of V.

Let's think of a situation in the perspective of a system (cylinder with a piston on top of it).

When the final volume is less than the initial volume, we have negative work. What does this mean?

It means that the system is not doing work! It is not investing any energy (negative work). So, work is being done on the system!

What if final volume is greater? that means the system is doing work! The system is investing energy to do work (positive). We describe this as work is being done by the system!

Understand how current, voltage and resistors behave in series and parallel circuits

I am pretty sure we all have memorized how current, voltage and resistors behave in series and parallel circuits. But, do you understand why they behave that way?

I would like to tackle its understanding today to the best of my ability.

The following explanation is adapted from http://physicsnet.co.uk/a-level-physics-as-a2/current-electricity/circuits/

Resistors in series and in parallel

Resistors in Series 

 When resistors are in series with each other there total resistance is just there individual resistance added together. 

Resistors in parallel 

 When resistors are in parallel with each other there total resistance is found using the equation below. 

The purpose of adding them in series is to make the total resistance bigger, while it is smaller in parallel. As more branches are added, you are lowering the resistance, which increases the total current. This is the reason why if you plug so many things to the outlet, the chance of having fire hazard increases! 

Current in series and parallel circuits

Conservation of charge – ” the total charge flowing into a junction of wires must equal the total charge flowing out of the junction”.

Kirchoff’s first law – “the sum of the currents flowing into a junction of wires must equal the sum of the currents flowing away from the junction of wires”.

  

Current in series circuits.

Current works differently than resistors. based on Kirchoff's first law, how much it flows out= how much it flows back in. Since there are no branches, the total current is the same throughout. 

This is why I1=I2=I3=I4....

Current in parallel circuits.

The total current flowing from the cell towards the branches in the circuit  must always equal the current flowing through each component in the branches of the circuit when they are added together. 

Here, we see the current gets branched out into 3 ways. So which mean the total current would be I1+I2+I3 ( remember Kirchoff's first law?)..

This is why Itotal= I1+I2+I3

  

If the components have different resistances then the current through each component may be different but it when you add them together they must add up to the total amount of current leaving the cell. 

Same reason as above: Itotal= I1+I2+I3 and I total must be 0.3A

Potential difference in series and parallel circuits

Kirchoffs second law – ” the sum of the Emf’s in any closed loop in a circuit must be equal to the sum of the potential differences in the closed loop in the circuit”.

Potential difference in a series circuit.

The total potential difference supplied by the cell is divided up between the components. If the components all have the same resistance they will have equal amounts of potential difference across them. 

When voltage meets a resistor, its voltage will decrease and its decreased amount will be based on the resistor. In this case, all resistors are the same so they decrease the same amount. However, at the end, they are all end up what was before, which is 12V.

This is why, Vtotal = V1+V2+V3= 12V

*Read this part after you finish the potential difference in a parallel circuit.

-If you think about it, for the following figure, if you add all of the components up, you get 12V, which corresponds to one of the components in the parallel circuit!

For example, if imagine you don't know the voltage for each of the component, but you know the resistor is the same. And you remember that voltage has to be the same (12V), so you could do something like 3x=12, where x=4! You just found the voltage for each of the component.

If the resistance are not equal they may have different amounts of potential difference across them but when added up they must always equal the p.d. supplied by the cell. 

Same reason as above. They have to add up to 12V at the end. 

   

 Potential difference in parallel circuits.

The potential difference supplied by the cell is the same potential difference as that across each component in the parallel circuit. 

Voltage doesn't work like Current. When voltage is branched out, the amount of voltage is the same (it doesn't split up into parts like current. Therefore, its 12V for each component

Thanks http://physicsnet.co.uk/a-level-physics-as-a2/current-electricity/circuits/ for the illustration and explanations. They allow me to understand the magical power that series and parallel circuits embody.

Understand why 4s orbital has a higher energy than 3d orbital

Why does 4s orbital has a higher energy than 3d orbitals?

RULE: The electron furthest away from the nucleus has the highest energy. <-- why?

1. Since nucleus (proton and neutron) attracts electron, it takes a huge amount of energy to pull electron from the ground state to n=4. This is why when electron moves to n=1 from n=4, it releases a tremendous amount of energy.

2. Since electron in 4s has a higher energy, it is quite unstable (we learn that lowest energy= stable and vice versa). As a result, it takes very little energy to remove electrons from 4s orbital. This is the trend you usually see in transition metal's electron configuration.

3. Since paired electrons repel against each other, 4s orbital  will have a higher energy.

Understand the signal for radioactive labeled element

Iodine is an essential element for the thyroid gland to produce thyroid hormone

Using radioactive labeled Iodine-131 as a tracer can tell us the activity of the thyroid gland in order to assess the health status of the human body.

How does this work?

Medical staffs usually would inject the patients with Iodine-131. Then, a gamma camera is used to collect and detect the emitted gamma rays (produced from the annihilation of the positron and an electron) from the thyroid gland.

What happens when you eat something that contains normal Iodine-127 in it, like shellfish?

Instead of collecting the radioactive labeled Iodine-131, the thyroid gland uses Iodine-127 to produce thyroid hormones. As a result, the signals detected from the thyroid gland do not reflect the actual amount of injected Iodine-131.

How does it look like in a graph?

Without the addition of Iodine-127, the graph would look like an ordinary decay, like a normal half life graph as shown below.

Taken from 

http://legacy.jefferson.kctcs.edu/techcenter/Classes/Physics/AtomicNuclearandModernPhysics/AtomicNuclearandModernPhysics8.html

With the addition of  Iodine-127, the signals dramatically fall depend on when you eat shellfish!
As you can see the ugly picture below drawn by me, there is a sudden decrease in the graph (circled in red). That is when you ate your shellfish!!! :)

Understand why the number of neutrons is greater than number of protons in heavy atoms

As we all know, nucleus is made of proton and neutron, in which protons are positively charged and neutrons are neutral. Since protons are positively charged, they repel each other when put together. Based on this, how do we get a stable atom?

The answer lies on strong nuclear force.

This type of force holds protons and neutrons together. Protons do exert this force with each other but electrostatic repulsion is stronger. Neutrons also exert this force but do not repel each other. Adding neutrons to the protons help them to overcome the repulsion, allowing them to stick together. Essentially, neutrons stabilize the nucleus ONLY at short distance (this force is only stronger than electrostatic repulsion at short distance) by attracting each other and protons equally with strong nuclear force.

However, as protons increase, more neutrons are needed to have strong nuclear force to overcome the repulsion. Eventually, atoms reach a point in which the repulsive force becomes way too huge for strong nuclear force to handle. This causes the nucleus to break apart into smaller nuclei, releasing a huge amount of energy in a process called fission. As a result, when you go down to the periodic table, you will notice that there are more neutrons than protons. 

Understand why water boils when its vapor pressure is equal to atomspheric pressure

Boiling point (when water boils) happens when vapor pressure is equal to atmospheric pressure. As long as vapor pressure is lower the atmospheric pressure, water WILL NOT BOIL. <-- What does that even mean?

For water to boil, the molecules must have enough kinetic energy to continuously escape from the surface of the water 

But how does that happen?

Boiling/evaporation happens when liquid molecules have enough kinetic energy to escape from liquid to the air. Since heat supplies energy, liquid molecules will eventually obtain enough energy to escape the liquid. Additionally, its vapor pressure exerted by liquid will be high because there are more and more gas molecules in the air colliding with each other.

What is blocking the liquid molecules from escaping?

The atmospheric pressure is preventing it. As mentioned previously, when liquid molecules try to escape, they will exert vapor pressure pushing against the atmospheric pressure. If the vapor pressure is not strong enough, then the atmospheric pressure will push the gas molecules back to liquid molecules; hence no bubbling. If its vapor pressure is equal or higher than atmospheric pressure, then now liquid molecules are free to escape from liquid to gas.