## Monday, July 29, 2019

### Unizor - Physics4Teens - Energy - Atoms and Chemical Reactions - Interat...

Notes to a video lecture on http://www.unizor.com

Interatomic Bonds

Atoms in a molecule are bonded together to form a stable chemical substance or compound.

The mechanism of bonding is quite complex and different for different
molecules. In fact, the complexity of these bonds is outside of the
scope of this course. However, certain basic knowledge about molecular
bonding and molecular structure is necessary to understand the following
lecture, where we will make certain calculations related to energy
produced or consumed in chemical reactions.

The key to a mechanism of bonding atoms into molecules lies in an internal structure of atoms.

For our purposes we can consider the orbital model of atom as consisting
of electrically positive nucleus and electrically negative electrons
circulating on different orbits around a nucleus. This is only a model,
not an exact representation of what's really happening inside the atom,
but this model gives relatively good results that correspond to some
simple experiments.

Two different particles can be found in a nucleus - positively charged
protons and electrically neutral neutrons. The number of protons inside a
nucleus and electrons circulating on different orbits around a nucleus
should be the same for electrically neutral atoms in their most common
state.

For reasons not well understood by many physicists, each orbit can have
certain maximum number of electrons that can circulate on it without
"bumping" into each other. The higher the orbit - the more electrons it
can hold. The lowest orbit can hold no more than 2 electrons, the next -
no more than 8, the next - no more than 14 etc.

Consider a few examples.

1. Let's consider the structure of a simplest molecule - the molecule of
hydrogen, formed by two atoms of hydrogen. Each hydrogen atom has one
electron on the lowest orbit around a nucleus. The maximum number of
electrons on this orbit is two, in which case the compound becomes much
more stable. So, two atoms of hydrogen grab each other and the two
electrons, each from its own atom, are shared by a couple of atoms, thus
creating a stable molecule of hydrogen with symbol H2. The bond between two atoms of hydrogen is formed by one pair of shared electrons, so structurally the molecule of hydrogen H2 can be pictured as

H−H.

2. Atom of oxygen has 8 electrons - 2 on the lowest orbit and 6 on the
next higher one. The next higher orbit is stable when it has 8
electrons. So, two atoms of oxygen are grabbing each other and share 2
out of 6 electrons on the outer orbit with another atom. So, each atom
has 4 "personal" electrons, 2 electrons that it shares with another atom
and 2 electrons that the other atom shares with it. Thus, the orbit
becomes full, all 8 spots are filled. The bond between two atoms of
oxygen is formed by two pairs of shared electrons, so structurally the
molecule of oxygen O2 can be pictured as

O=O

(notice double link between the atoms).

3. Our next example is gas methane. Its molecule consists of one atom of
carbon (6 electrons, 2 of them on the lowest orbit, 4 - on the next
one) and 4 atoms of hydrogen (1 electron on the lowest orbit of each
atom). Obviously, having only 4 electrons on the second orbit, carbon is
actively looking for electrons to fill the orbit. It needs 4 of them to
complete an orbit of 8 electrons. Exactly this it finds in 4 atoms of
hydrogen that need to complete their own lowest orbit. Sharing
electrons, one atom of carbon and 4 atoms of hydrogen fill their
corresponding orbits, thus creating a molecule of methane CH4 with can be pictured as

H

|

H−C−H

|

H

4. Carbon dioxide molecule contains 1 atom of carbon, that needs 4
electrons to complete its orbit, and 2 atoms of oxygen, each needs 2
electrons to complete its orbit: CO2. By
sharing 2 electrons from each atom of oxygen with 4 electrons from atom
of carbon they all fill up their outer orbit of electrons and become a
stable molecule, pictured as

O=C=O

(notice double link between the atoms).

5. Ethanol molecule contains 2 atoms of carbon, 1 atom of oxygen and 6 atoms of hydrogen connected as follows

H   H

|     |

H−C−C−O−H

|     |

H   H

(notice single bond between atoms of carbon and oxygen in ethanol, while
the bond between them in carbon dioxide has double link)

6. Hydrogen peroxide molecule contains 2 atoms of hydrogen and 2 atoms of oxygen connected as follows

H−O−O−H

(notice single bond between atoms of oxygen, not like in a molecule of oxygen)

Numerous examples above illustrate that bonds between atoms can be
different, even between the same atoms in different molecules. That's
why it is important to understand the structure of molecules, how
exactly the atoms are linked and what kind of links exist between them.
This is the basis for calculation of the amount of energy produced or
consumed by chemical reactions that rearrange the atoms from one set of
molecules to another.

Obviously, bonds O−O and O=O are different.
The first one is facilitated by one shared electron, the second one - by
two. The amounts of energy, needed to break these bonds, are different
too. Therefore, when calculating the energy of chemical reaction, it's
important to understand the kind of bond between atoms in each separate
case.

## Tuesday, July 23, 2019

### Unizor - Physics4Teens - Energy - Chemical Energy of Atomic Bonds

Notes to a video lecture on http://www.unizor.com

Energy of Atomic Bonds

in Molecules

In this lecture we will analyze the energy aspect of chemical reactions.

Consider the reaction of burning of methane. This gas is used in regular
gas stoves, so the reaction happens every time we cook something.

A molecule of methane consists of one atom of carbon C and four atoms of hydrogen H, the chemical formula of methane is CH4.

You can imagine a molecule of methane as a tetrahedron, in its center is
an atom of carbon and on each of its four vertices is an atom of
hydrogen.

A molecule of oxygen, as we know, consists of two atoms of oxygen and has a chemical formula O2.

As a result of the reaction of burning of methane, water and carbon dioxide are produced, according to the following equation:

CH4 + 2O2 = 2H2O + CO2

So, during this reaction

(a) four atomic bonds between carbon and hydrogen in one molecule of methane are broken,

(b) one atomic bond in each molecule of oxygen (out of two) are broken,

(c) two atomic bonds between hydrogen and oxygen in each molecule of water (out of two) are created,

(d) two atomic bonds between carbon and oxygen in a molecule of carbon dioxide are created.

Amounts of potential energy of the different atomic bonds are
experimentally determined, which would lead to calculation of the amount
of chemical energy released (for exothermic) or consumed (by
endothermic) reaction.

To make experiments to determine potential energy of the bonds inside a
molecule, we have to make experiments with known amounts of components
in chemical reaction. The reaction above includes one molecule of
methane and two molecules of oxygen. Obviously, we cannot experiment
with one or two molecules. The solution is to experiment with proportional amounts of components, say, 1 million of molecules of methane and 2 million of molecules of oxygen.

To explain how to do this, we have to get deeper into atoms. Physics
models atoms as consisting of three kinds of elementary particles -
protons (electrically positively charged), neutrons (electrically
neutral) and electrons (electrically negatively charged). This is a
relatively simple model, that corresponds to most of experiments, though
the reality is more complex than this. For our purposes we can view
this model of atom as a nucleus, that contains certain number of protons
and neutrons, and a number of electrons circulating the nucleus on
different orbits.

Electrons are very light relatively to protons and neutrons, so the mass
of an atom is concentrated, mostly, in its nucleus. Protons and neutron
have approximately the same mass, which is called atomic mass unit. So, the mass of an atom in atomic mass units
("atomic weight") is equal to the number of protons and neutrons in its
nucleus. This mass is known for each element of the Periodic Table of
Mendeleev, that is for each known atom.

For example, it is determined that atom of hydrogen H has atomic weight of 1 atomic unit, atom of carbon C has atomic weight of 12, atom of oxygen O has atomic weight 16.

Knowing atomic weights of atoms, we can calculate atomic weight of molecules. Thus, the atomic weight of a molecule of methane CH4 is 12+4=16. Atomic weight of a molecule of oxygen O2 is 16+16=32. Atomic weight of water H2O is 2+16=18.

Now we can take components of any chemical reaction proportional to the
atomic weight of corresponding molecules, which will result in
proportional number of molecules. For example, not being able to
experiment with one molecule of methane CH4 and two molecules of oxygen O2, we can experiment with 16 gram of methane and 64 gram
of oxygen, and the proportionality of the number of molecules will be
preserved - for each molecule of methane there will be two molecules of
oxygen.

As you see, taking amount of any mono-molecular substance in grams
equaled to the atomic weight of the molecules of this substance (called a
mole) assures taking the same number of molecules, regardless of the substance. This number is the Avogadro Number and is equal to N=6.02214076·1023.

Thus, one mole of methane CH4 (atomic weight of C is 12, atomic weight of H is 1) weighs 16g, one mole of silicon Si2 (atomic weight of Si is 14) weighs 28g, one mole of copper oxide CuO (atomic weight of Cu is 64, atomic weight of O
is 16) weighs 80g etc. And all those amounts of different substances
have the same number of molecules - the Avogadro number (approximately,
of course).

The theory behind the atomic bonds inside a molecule is quite complex
and is beyond the scope of this course. Based on this theory and
experimental data, for many kinds of atomic bonds there had been
obtained an amount of energy needed to break these bonds, that is its
inner chemical energy.

Thus, chemical energy of atomic bonds inside a mole of methane CH4
is 1640 kilo-joules (because a molecule of methane has 4 bonds between
carbon and each atom of hydrogen, each bond at 410KJ), inside a molecule
of oxygen O2 - 494 kilo-joules (1 bond between 2 atoms oxygen at 494KJ), inside a molecule of carbon dioxide CO2 is 1598 kilo-joules (2 bonds between carbon and each atom of oxygen, each 799KJ), inside a molecule of water H2O is 920 kilo-joules (2 bonds between oxygen and each atom of hydrogen, each 460KJ).

Let's go back to methane burning:

CH4 + 2O2 = 2H2O + CO2

This chemical reaction converts 1 mole of methane (16g) and 2 moles of
oxygen (64g) into 1 mole of carbon dioxide (44g) and 2 moles of water
(36g).

The energy we have to spend to break the atomic bonds of 1 mole of methane and 2 moles of oxygen, according to above data, is

Ein = 1640 + 2·494 = 2628 KJ

The energy we have to spend to break atomic bonds of 2 moles of water and 1 mole of carbon dioxide, according to above data, is

Eout = 2·920 + 1598 = 3438 KJ

The net energy is

Enet = 2628 − 3438 = −810 KJ

This net energy is the amount of thermal energy released by burning 16g
of methane, using 64g of oxygen, obtaining as a result 44g of carbon
dioxide and 36g of water.

## Thursday, July 18, 2019

### Unizor - Physics4Teens - Energy - Atoms

Notes to a video lecture on http://www.unizor.com

Atoms and Chemical Reaction

Discussing mechanical energy, we analyzed the movement of objects.

When talking about thermal energy (heat), we had to go deeper inside the objects and analyzed the movement of molecules, the smallest parts of objects that retained the properties of objects themselves.

Now we go even deeper, inside the molecules, in search of new kinds of energy.

The components of molecules are called atoms. Currently there are more than 100 kinds of atoms, classified in the Mendeleev's Periodic Table.

Different combinations of these atoms in different quantities make up all kinds of molecules, each with its own properties.

In some cases a single atom makes up a molecule. For example, a single atom of iron (denoted by symbol Fe) makes up a molecule of iron.

In some other cases a pair of atoms of the same type makes up a molecule. For example, two atoms of oxygen (denoted by symbol O) make up a molecule of oxygen (denoted by symbol O2).

In more complicated cases a few atoms of different types make up a molecule. For example, two atoms of hydrogen (denoted by symbol H) and one atom of oxygen (O) make up a molecule of water (H2O).

One of the most complicated molecules that contains many elements in
different quantities is a molecule of protein that has about half a
million of atoms.

Chemical energy is a potential energy of bonds between atoms that hold them together in a molecule.

Chemical reaction is a process of re-arranging of atoms in a group of molecules, getting, as a result, a group of other molecules.

During chemical reactions some bonds between atoms are broken and some are created. Therefore, the energy might be either released or consumed in the process of chemical reaction.
This energy, stored in the molecules as potential energy of atomic
bonds and released or consumed during chemical reaction, is classified
as chemical energy.

Let's consider a few examples of chemical energy.

1. Coal burning

One molecule of carbon, that consists of one carbon atom C, and one molecule of oxygen, that consists of two oxygen atoms O2, when brought together and lit up, will join into one molecule of carbon dioxide CO2
in the process of burning. After the chemical reaction of burning is
initiated, it will maintain itself, as the process of burning produces a
flame that lights up new molecules of carbon, joining them with oxygen.

The chemical reaction

C + O2 = CO2

is endothermic (consumes heat energy) in the very beginning, when we
have to light up the carbon, but, as soon as the reaction started, it
becomes exothermic, that is it produces heat energy, because the
potential energy of atoms inside molecules of carbon and oxygen together
is greater than potential energy of atoms inside a molecule of carbon
dioxide.

2. Making water from hydrogen and oxygen

Two molecules of hydrogen, each consisting of two hydrogen atom H2, and one molecule of oxygen, that consists of two oxygen atoms O2, when brought together and lit up, will join into two molecules of water H2O
in the process of hydrogen burning. After the chemical reaction of
burning is initiated, it will maintain itself, as the process of burning
produces a flame that lights up new molecules of hydrogen, joining them
with oxygen.

The chemical reaction

2H2 + O2 = 2H2O

is endothermic (consumes heat energy) in the very beginning, when we
have to light up the hydrogen, but, as soon as the reaction started, it
becomes exothermic, that is it produces heat energy, because the
potential energy of atoms inside two molecules of hydrogen and one
molecule of oxygen together is greater than potential energy of atoms
inside two molecules of water.

3. Photosynthesis

This is a complicated process, during which the light from sun, air
components (such as carbon dioxide, nitrogen and oxygen), water and
whatever is in the soil are converted by the plants into chemical energy
that maintains their life. This is an endothermic process, and, as its
result, plants grow. In most cases they consume carbon dioxide from the
air, break it into carbon and oxygen, consume the water from the soil,
break it into hydrogen and oxygen (they need sun's radiation energy to
break the molecules of CO2 and H2O),
use the carbon, hydrogen and part of oxygen to produce new organic
molecules they consist of and release the unused oxygen back into
atmosphere.

4. Battery

Battery consists of three major components: anode, cathode and electrolyte
in-between anode and cathode. As a result of a chemical and
electro-magnetic reaction between the molecules of anode and
electrolyte, some electrons are transferred from anode to electrolyte.
Then, as a result of a chemical and electro-magnetic reaction between
the molecules of cathode and electrolyte, some electrons are transferred
from electrolyte to cathode. As the result, there are extra electrons
on the cathode, which were taken from the anode, thus creating
electrical potential.

These simple examples explain the general mechanism of chemical energy,
released or consumed in the course of chemical reaction, that transforms
molecules by rearranging their atoms' composition. As a result of a
chemical reaction and change in the atomic composition of molecules,
potential energy of bonds between atoms in molecules is changing. If the
total potential energy of the resulting molecules is greater than the
potential energy of the bonds inside original molecules, the process is
endothermic, it consumes energy. In an opposite case the process is
exothermic, it produces energy.

The exothermic process of extracting chemical energy using chemical
reaction is the key to getting energy from gasoline in the car engine,
producing heat and light in the fireplace by burning wood, it's the
source of energy in all living organisms, including humans. We exist
because our body knows how to extract chemical energy from the food.

## Monday, July 8, 2019

### Unizor - Physics4Teens - Energy - Heat Transfer Problems

Notes to a video lecture on http://www.unizor.com

Heat Transfer - Problems

Problem 1

Determine the power of the heat source inside the room required to
maintain a certain difference between inside and outside air
temperature, given the following:

(a) the difference between inside and outside temperature δ=Tout−Thome

(b) the room has only one wall facing the outside air, and the area of this wall is A

(c) the thickness of the wall is L

(d) the wall is made of solid material with a coefficient of thermal conductivity k.

Solution

Let x be the distance from a point inside the wall to its surface facing the room.

The T(x) is a temperature at this point as a function from this distance.

To be equal to Thome at the surface facing the room and to be Tout at the surface facing the outside and to be linearly changing from one value to another inside the wall of the thickness L, the temperature inside the wall at distance x from the surface facing the room should be

T(x)=Thome+(Tout−Thome)·x/L

From this we can determine the heat flux through the wall at a distance x, using the Fourier's law of thermal conduction:

Q(x,A) = −k·A·dT(x)/dx =

= −k·A·(Tout−Thome)/L =

= −k·A·δ/L

That is exactly how much heat we need to maintain the difference between temperature in the room and outside.

Problem 2

Calculate the heating requirement of the room with only one concrete
wall facing outside with no windows, assuming the following:

(a) the temperature in the room must constantly be Troom=20°C

(b) the temperature outside is also constant Tout=5°C

(c) the thickness of the concrete wall facing outside is L=0.2m

(d) the area of the wall facing outside is A=12m²

(e) heat conductivity of concrete is k=0.6W/(m·°K)

Solution

Using the above, we can determine the heat flux through the wall at a distance x:

Q(x,A) = −k·A·δ/L

(for any distance x from the surface of the wall that faces the room)

Outside surface of the wall is at 5°C, inside is at 20°C.

So, δ=15°.

Therefore, the heat flux through the wall (at any distance from the inside surface) will be

Q = 0.6·12·15/0.2 = 540W

That is exactly how much heat we need to maintain the temperature in the room.

Problem 3

Our task is to determine the law of cooling of a relatively small hot
object immersed in the cool infinitely large reservoir with liquid or
gaseous substance.

We assume the volume of substance this object is immersed in to be
"infinite" to ignore its own change of temperature related to heat
emitted by our hot object.

This law of cooling should be expressed in terms of object's temperature T as a function of time t, that is, we have to find the function T(t).

Assumptions:

(a) the initial temperature of the object at time t=0 is assumed to be T0

(b) the object has a shape of a thin flat square (so, its temperature is changing simultaneously in all its volume) of size LxL and mass m

(c) the specific heat capacity of the object's material is C

(d) the temperature of the substance surrounding our object is constant and equals Ts

(e) the convective heat transfer coefficient of the substance around our object is h.

Solution

Consider a small time interval from t to t+Δt.

The temperature of an object is T(t), while the temperature of the substance around it is constant Ts.
Then the amount of heat transferred from our object to the substance
around it per unit of time per unit of its surface area is proportional
to the difference in temperatures with the convective heat transfer coefficient as a factor:

q = −h·[T(t)−Ts]

Since total surface area of our thin flat square, ignoring its thickness, is 2L² and the time interval we consider is Δt, the total amount of heat transferred by our object through its surface during this time period is

ΔQ(t) = −2L²·h·[T(t)−Ts]·Δt

This is amount of heat taken away by the substance from our object during a time interval Δt.

The same amount of heat is lost by the object, taking its temperature from T(t) to T(t+Δt).

As we know, changes of heat and temperature are proportional and related to the object mass and specific heat capacity:

ΔQ(t) = C·m·ΔT

where ΔT = T(t+Δt)−T(t).

Equating the amount of heat lost by our object to the amount of heat
carried away by convection of the substance around it, we have come to
an equation

−2L²·h·[T(t)−Ts]·Δt =

= C·m·
[T(t+Δt)−T(t)]

Dividing both parts by Δt, diminishing this time interval to zero and using a derivative by time t to express the limit, we get the following differential equation

−2L²·h·[T(t)−Ts] =

= C·m·
dT(t)/dt

To solve it, let's make two simple substitutions:

(a) A = 2h·L²/(C·m)

(b) X(t) = T(t) − Ts

Then, since Ts is constant,

dT(t)/dt = dX(t)/dt

and our differential equation looks like

dX(t)/dt = −A·X(t)

To solve this, we convert it as follows:

dX(t)/X(t) = −A·dt

d[ln(X(t))] = −A·dt

Integrating:

ln(X(t))] = −A·t + B,

where B is any constant, defined by initial condition

X(0)=T(0)−Ts=T0−Ts.

From the last equation:

X(t) = eB·e−A·t

Using initial condition mentioned above,

X(t) = (T0−Ts)·e−A·t

Since X(t)=T(t)−Ts

T(t) − Ts = (T0−Ts)·e−A·t

or

T(t) = Ts + (T0−Ts)·e−A·t

where A = 2h·L²/(C·m)

So, the difference in temperature between a hot object and infinitely
large surrounding substance is exponentially decreasing with time.