ideal gas

5

Chapter 1.8 - Ideal Gas Law pt.1: the analogy  // Science Scribbles A-Level / IB HL Chemistry collection

(Click here for Ideal gas law part 2)

Hey again! I’m sitting in the children section of the library, so I decided that kids running around in a room would be a good way to visualize the ideal gas equation. Hope this helped you :D Stay tuned for part two, where I explain how to solve problems concerning the ideal gas law.

Remember the main difference between real gases and an ideal gas is that there are no intermolecular forces in an ideal gas - meaning there is no liquid phase when you cool it down. A real gas is similar to an ideal gas under high temperature and low pressure. :D

P.S. Lately I’ve started receiving a lot of requests, but unfortunately I do not have time to draw them all at once - so I’m only going to draw the ones that are most requested, I’m really sorry!

Hello Studyblr Community,

Just wanted to send out a little note - a friendly reminder - that if you have any troubles in a chemistry course or chemistry related topic feel free to send me a message. While my studyblr is here for personal motivation to finish up my undergrad, it’s also here as a resource for anyone who struggles or needs some simple help in chemistry. So far I have taken both general chemistries which cover topics ranging from unit conversions, titrations, ideal gas laws, molecular geometry, and intermolecular forces, *The list continues and I have multiple study/cheat sheets for many of these topics since my lecture was student-based teaching. Also, I have completed the first semester of organic chemistry that includes resonance structures, chirality, nomenclature, SN1/2 and E1/2 reactions, and alcohol synthesis. Right now I am enrolled in the second semester of organic chemistry (currently making a solid B in case you wanted to know how reliable I am with my knowledge) and have covered ether synthesis, aromatic nucleophilic/electrophilic substitution, activation/deactivation on the aromatic ring, amine synthesis, aldehyde/keytone synthesis, carboxylic synthesis. Next semester I will begin advance organic structure studies that include UV spectrum, proton and carbon 13 NMR, mass spectrum, and IR spectrum. Though I am already confident with handling those instruments and can help anyone who needs an understanding of how to label peaks or knowing what an unknown compound contains. On top of that, I will be taking analytical chemistry next semester as well. 

Of course, the list continues because I will always try my best to answer any chemistry related questions that my followers have. (Google does wonders for me and I have a good way of finding amazing study guides) So please don’t be shy when asking questions or correcting me when I’m wrong. I don’t have my degree yet in chemistry so I’m not always correct! :) Love you guys and keep up the good work. [Link to my ask box]

*It would be awesome if everyone could spread this little note so I can help anyone out who needs it. I hate to see students struggle in chemistry when I am currently on my way to becoming a teacher.  

Thermodynamics

Heat capacity

See previous posts about thermal physics

Heat capacity c is a measure of the amount of thermal energy Q can be put into a system before we see a change in its temperature ΔT. It is defined by the equation

where ΔT may be defined as ΔT = T - T0 for an initial temperature T0 and a final temperature T, so

Therefore, if you put 5 J of energy into some volume of liquid, we’ll call it X, which is at an initial temperature T0 = 20°C and observed its temperature change to T = 25°C then it would have a heat capacity cX

Specific heat capacity

This is particularly useful for engineering purposes because a heat capacity can be used to characterise gases and materials etc. For example, the specific heat capacity c of a material is found using its heat capacity per unit mass:

(note that this equation assumes that the heat capacity is independent of mass – i.e. for no phase transitions).

could you please ask your followers to click on the link/watch my final video project for chemistry and to give our video a thumbs up? the link is https://www.youtube.com/watch?v=-mC1wUoUMc8 . we get graded on how many views/likes we get, so I’d really appreciate it! :) thanks so much

So you guys should totally watch this chemistry video that raps about the ideal gas laws. :D

It helps out students, so that’s cool as well.

Quantum Physics

Finding the expectation value

Cont’d from “Expectation value general form

The expectation value can be well understood by studying the mathematics applied to particular scenarios. In this post we will apply a quantum mechanic approach to find the expectation value of measurement.

Particle in a box example

Not to be confused with “Pressure of an ideal gas

This system is often known as the infinite square well.

Consider a particle with wavefunction in position representation given by

where N is a normalisation factor, confined to a 1-dimensional box in 0 ≤ x L.

We measure its momentum – what is the expected value of this measurement?

Thus, we need to find the expectation value of momentum in the x-direction;

since we can assume that the particle is entirely contained within the range 0 ≤ x L the limits can be adjusted to reflect this,

First, we’ll find the probability; |⟨ x | ψ ⟩|2:

and since we know that ⟨ ψ | x ⟩ = ⟨ x | ψ ⟩* we can find the complex conjugate of the given expression. So, we find that

which can be multiplied by the original expression to find

and since e0 = 1,

Now we must find px. Let’s look at the eigen-equation of its operator:

whose calculation provides the eigenvalue px. We know that this operator is given by

which we can act onto the wavefunction to get

for which we can calculate the derivative

and we know that

so

implying that

Thus, combining these factors into the expectation value equation, we get

and so,

Hopefully, the square well scenario will be examined in much more detail in future posts − including solving the Schrödinger equation for different scenarios.