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# Category Archives: Chemistry

### Reasoning

(from Modern Chemistry, Davis, HRW)

### As shown below, the coefficients in a chemical reaction involving gases indicate the relative numbers of molecules, the relative numbers of moles, and the relative volumes. ## As an equation

### or ## Example problems

### V1 / n1 = V2 / n2

2.00 L / 0.500 mol = 2.70 L / x

x = 0.675 mol

### 0.675 mol – 0.500 mol = 0.175 mol

0.175 mol x 4.00 g/mol = 0.7 grams of He added

### We can perform a calculation using Avogadro’s Law:

V1 / n1 = V2 / n2

Let’s assign V1 to be 1 L and V2 will be our unknown.

Let us assign 1 mole for the amount of neon gas and assign it to be n1.

The mass of argon now added is exactly equal to the neon, but argon has a higher gram-atomic weight (molar mass) than neon. Therefore less than 1 mole of Ar will be added. Let us use 1.5 mol for the total moles in the balloon (which will be n2) after the Ar is added. (I picked 1.5 because neon weighs about 20 g/mol and argon weighs about 40 g/mol.)

1 / 1 = x / 1.5

x = 1.5

### V1 / n1 = V2 / n2

 5.120 L 18.10 L –––––––– = –––––– 8.500 mol x

x = 30.05 mol <— total moles, not the moles added

30.05 – 8.500 = 21.55 mol (to four sig figs)

## Charles’s Law

### This relationship can be written as: ### This relationship can be written as: ### Important! This is not a law of physics! Rather, this is a generally useful rule, which is only valid when gas temperature and pressure is low enough for the atoms to usually be far apart from each other.  As we begin to deal with more extreme cases, this rule doesn’t hold up.

Let’s see this in action! https://www.grc.nasa.gov/WWW/K-12/airplane/aglussac.html

## Origin

### Named after Jacques Alexandre César Charles (1746 – 1823)  a French inventor, scientist, mathematician, and balloonist. Just so we’re all clear on this, he was kind of a mad scientist. And I say that with the utmost approval! Contemporary illustration of the first flight by Prof. Jacques Charles with Nicolas-Louis Robert, December 1, 1783. Viewed from the Place de la Concorde to the Tuileries Palace (destroyed in 1871)

.Apps

Charles’s law app

## Learning standards

Massachusetts Science and Technology/Engineering Curriculum Framework

8.MS-PS1-4. Develop a model that describes and predicts changes in particle motion, relative spatial arrangement, temperature, and state of a pure substance when thermal energy is added or removed.

Next Generation Science Standards

MS-PS1-4. Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.

College Board Standards

Objective C.1.5 States of Matter

C-PE.1.5.2 Explain why gases expand to fill a container of any size, while liquids flow and spread out to fill the bottom of a container and solids hold their own shape. Justification includes a discussion of particle motion and the attractions between the particles.

C-PE.1.5.3 Investigate the behavior of gases. Investigation is performed in terms of volume (V ), pressure (P ), temperature (T ) and amount of gas (n) by using the ideal gas law both conceptually and mathematically.

Common Core Math

Analyze proportional relationships and use them to solve real-world and mathematical problems.

Ratios & Proportional Relationships

Ratios & Proportional Relationships

CCSS.MATH.CONTENT.7.RP.A.2

Recognize and represent proportional relationships between quantities.

CCSS.MATH.CONTENT.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

CCSS.MATH.CONTENT.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

## Boyle’s law (gas laws)

A general relationship between pressure and volume: Boyle’s Law

As the pressure on a gas increases, the volume of the gas decreases because the gas particles are forced closer together.

Conversely, as the pressure on a gas decreases, the gas volume increases because the gas particles can now move farther apart.

Example: Weather balloons get larger as they rise through the atmosphere to regions of lower pressure because the volume of the gas has increased; that is, the atmospheric gas exerts less pressure on the surface of the balloon, so the interior gas expands until the internal and external pressures are equal.

from Libretexts, Chemistry, 5.3: The Simple Gas Laws: Boyle’s Law, Charles’s Law and Avogadro’s Law, CC BY-NC-SA 3.0.

This means that, at constant temperature, the pressure (P) of a gas is inversely proportional to the volume (V).

PV = c

Important! This is not a law of physics! Rather, this is a generally useful rule, which is only valid when gas temperature and pressure is low enough for the atoms to usually be far apart from each other.  As we begin to deal with more extreme cases, this rule doesn’t hold up.

Let’s see the relationship in action, here: Early scientists explored the relationships among the pressure of a gas (P) and its temperature (T), volume (V), and amount (n) by holding two of the four variables constant (amount and temperature, for example), varying a third (such as pressure), and measuring the effect of the change on the fourth (in this case, volume).

The history of their discoveries provides several excellent examples of the scientific method.

The Irish chemist Robert Boyle (1627–1691) carried out some of the earliest experiments that determined the quantitative relationship between the pressure and the volume of a gas. Boyle used a J-shaped tube partially filled with mercury.

In these experiments, a small amount of a gas or air is trapped above the mercury column, and its volume is measured at atmospheric pressure and constant temperature. More mercury is then poured into the open arm to increase the pressure on the gas sample.

The pressure on the gas is atmospheric pressure plus the difference in the heights of the mercury columns, and the resulting volume is measured. This process is repeated until either there is no more room in the open arm or the volume of the gas is too small to be measured accurately. Details: Boyle’s Experiment Using a J-Shaped Tube to Determine the Relationship between Gas Pressure and Volume.

(a) Initially the gas is at a pressure of 1 atm = 760 mmHg (the mercury is at the same height in both the arm containing the sample and the arm open to the atmosphere); its volume is V.

(b) If enough mercury is added to the right side to give a difference in height of 760 mmHg between the two arms, the pressure of the gas is 760 mmHg (atmospheric pressure) + 760 mmHg = 1520 mmHg and the volume is V/2.

(c) If an additional 760 mmHg is added to the column on the right, the total pressure on the gas increases to 2280 mmHg, and the volume of the gas decreases to V/3

(This section from from Libretexts, Chemistry, 5.3: The Simple Gas Laws: Boyle’s Law, Charles’s Law and Avogadro’s Law, CC BY-NC-SA 3.0)

## Learning standards

Massachusetts Science and Technology/Engineering Curriculum Framework

8.MS-PS1-4. Develop a model that describes and predicts changes in particle motion, relative spatial arrangement, temperature, and state of a pure substance when thermal energy is added or removed.

Next Generation Science Standards

MS-PS1-4. Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.

College Board Standards

Objective C.1.5 States of Matter

C-PE.1.5.2 Explain why gases expand to fill a container of any size, while liquids flow and spread out to fill the bottom of a container and solids hold their own shape. Justification includes a discussion of particle motion and the attractions between the particles.

C-PE.1.5.3 Investigate the behavior of gases. Investigation is performed in terms of volume (V ), pressure (P ), temperature (T ) and amount of gas (n) by using the ideal gas law both conceptually and mathematically.

Common Core Math

Analyze proportional relationships and use them to solve real-world and mathematical problems.

Ratios & Proportional Relationships

Ratios & Proportional Relationships

CCSS.MATH.CONTENT.7.RP.A.2

Recognize and represent proportional relationships between quantities.

CCSS.MATH.CONTENT.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

CCSS.MATH.CONTENT.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

## Oils

### PHET Polar molecules app http://catalog.flatworldknowledge.com/bookhub/4309?e=averill_1.0-ch08_s09

### The lipophilic end likes to stick to oil molecules, but hates sticking to water, ### Made with many C and H atoms https://cedarbraechemistry.wikispaces.com/5.1+Thanoja-+Combustion+of+Hydrocarbons

### Oils are usually flammable. Here we see oils in an orange skin interacting with a candle. ## Rotary catalytic mechanism of mitochondrial ATP synthase

Introduction

(Text in this section adapted from “ATP synthase.” Wikipedia, The Free Encyclopedia. 27 Mar. 2019.)

## Molecular animation of ATP synthase

### Here is a three dimensional animation of all the proteins working together in this complex. We see it situated in a lipid bilayer (organelle membrane.) ### Here is another animation of a similar complex. Video

Rotary catalytic mechanism of mitochondrial ATP synthase

## Learning Standards

(TBA)

Biology, Chemistry, Simple machines

## Elements necessary for life

### Phosphorus – Necessary to make DNA and RNA. Also a component of bones and teeth. Microbial Genomics and the Periodic Table, Lawrence P. Wackett, Anthony G. Dodge and Lynda B. M. Ellis

. Microbial Genomics and the Periodic Table, Lawrence P. Wackett, Anthony G. Dodge and Lynda B. M. Ellis

## What is Lewis Theory?

### This is Lewis theory. But this Lewis approach is not complete and it only gives hints about the underlying quantum mechanics, a world observed through spectroscopy and mathematics.

Patterns

Consider the pattern shown in Diagram-1: ### Now expand the view slightly and look at Diagram-2 ### Zoom out a bit and look at the pattern in Diagram-3, the anomaly disappears ### But then look at Diagram-4. The purple patch on the upper right hand side does not seem to fit the pattern and so it may represent anomaly ### But zooming right out to Diagram-5 we see that everything is part of a larger regular pattern. Image from dryicons.com, digital-flowers-pattern

### As chemists we attempt to ‘explain’ many of these patterns in terms of electron accountancy and magic numbers.

Caught In The Act: Theoretical Theft & Magic Number Creation

The crucial time for our understand chemical structure & bonding occurred in the busy chemistry laboratories at UC Berkeley under the leadership of G. N. Lewis in the early years of the 20th century.

Lewis and colleagues were actively debating the new ideas about atomic structure, particularly the Rutherford & Bohr atoms and postulated how they might give rise to models of chemical structure, bonding & reactivity.

Indeed, the Lewis model uses ideas directly from the Bohr atom. The Rutherford atom shows electrons whizzing about the nucleus, but to the trained eye, there is no structure to the whizzing. Introduced by Niels Bohr in 1913, the Bohr model is a quantum physics modification of the Rutherford model and is sometimes referred to the Rutherford–Bohr model. (Bohr was Rutherford’s student at the time.) The model’s key success lay in explaining (correlating with) the Rydberg formula for the spectral emission lines of atomic hydrogen.

• ### The chemistry fork started when Lewis published his first ideas about the patterns he saw in chemical bonding and reactivity in 1916, and later in a more advanced form in 1923. Lewis realised that electrons could be counted and that there were patterns associated with structure, bonding and reactivity behaviour.These early ideas have been extensively developed and are now taught to chemistry students the world over. This is Lewis theory.

_____________________________________________________

Lewis Theory and Quantum Mechanics

### Quantum mechanics and Lewis theory are both concerned with patterns. However, quantum mechanics actively causes the patterns whereas Lewis theory is passive and it only reports on patterns that are observed through experiment.

We observe patterns of structure & reactivity behaviour through experiment.

Lewis theory looks down on the empirical evidence, identifies patterns in behaviour and classifies the patterns in terms of electron accountancy& magic numbers. Lewis theory gives no explanation for the patterns.

In large part, chemistry is about the behaviour of electrons and electrons are quantum mechanical entities. Quantum mechanics causes chemistry to be the way it is. The quantum mechanical patterns are can be:

• Observed using spectroscopy.
• Echoes of the underlying quantum mechanics can be seen in the chemical structure & reactivity behaviour patterns.
• The patterns can be calculated, although the mathematics is not trivial.

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