Determining the Molar Volume of a Gas

Measurable Properties of Gases:

A gas is said to be a state of matter which can be differentiated from solid and liquid due to its relatively low density, viscosity, and its ability to contract and expand or diffuse with respect to change in the temperature and pressure. The characteristics of the gases can be described using four important properties, which are collectively termed as called as the measurable properties of gases.

The measurable properties of gases are
1.Volume of the gas
2. Pressure of the gas
3. Temperature of the gas
4. Amount of the gas (mass)

Volume

Volume which is one of the measurable property of the gas is denoted by the letter 'V'. It is expressed in litres(L) , milliliters(mL), cubic centimeters(cm³),  cubic metres(dm³)  and cubic decimetres(dm³).
1litre = 1000 millilitres  , 1 millilitre = 1cubic centimetre and 1 cubic metre = 1000 cubic centimetre
1L  = 1dm³ = 10^–3 m³   = 1000 mL = 1000000 cm³
The volume of the gas depends on the pressure, temperature and the amount of gas present.The measurement of volume of gas requires the measurement of volume of the container in which the gas is present.

Pressure

Pressure is the next important measurable property of the gas which is denoted by the letter 'P'. Pressure of the gas is the force exerted by the gas per unit area.It depends on the kinetic energy of the molecules. As the kinetic energy inturn depends on temperature, the pressure is directly proportional to the temperature of the gas.
Pressure (P) = Force/Area = (Mass) (Acceleration)/Area
Pressure is commonly expressed in atmospheres, mm of Hg, torr, bar, and K.Pa.
1atm = 760mm of Hg = 760 torr = 1.01325 bar = 101.325 kPa = 101.326 x 10³ N m^-2  
Pressure of the gas can be measured by Barometer.    

Temperature

The temperature of the gas is denoted by  the letter 'T'.The temperature of a gas depends on the kinetic energy of the gas.The gases  expand on increasing the temperature.The temperature of the gas is generally expressed in Fahrenheit (F^o), Centigrade degree (^oC)  or celsius degree and Kelvin (K).
   K = ^oC + 273  and ^oC/5 = F^o–32/9
The temperature is measured by the help of a Thermometer.

Amount of gas

Amount of gas or the mass is a measurable property of the gas.The mass of the gas is related to the number of moles of the gas. The mass of the gas is generally expressed in kilograms(Kg) or grams(g).
number of moles (n) = mass of the gas/ molar mass of the gas
                                    n = m/M
The mass of the gas can be found through weighing. The mass of the gas can be obtained by subtracting the mass of the container in which the gas is present from the total mass.

Determining The Molar Volume of a Gas:

The Ideal gas law states that,
PV=nRT
Where P is pressure,V is volume, n is number of moles,R is gas constant and T is temperature.
At STP,which means standard temperature and pressure,the values of  temperature and pressure are 273 K [0 C] and 1 atm respectively.
If these values are substituted,we get,
1xV=nRx273
also substitute n= one mole and substitute value of  R= 0.082 Liter-Atmospheres per Mole-Degree Kelvin,
we get,
V=22.4 L
So one mole of a gas at STP would occupy 22.4L of volume.This is called as molar volume of a gas.
So irrespective of a gas,its one mole would occupy 22.4L of volume.

Illustration on Determining the Molar Volume of a Gas :

Find the volume of 88g of CO₂ at STP.
First find moles of CO_2. in 88g of CO_2.
Moles=Mass in g/Molar mass
=88/44
=2 moles
Volume of 2 moles= 2 x 22.4
=44.8 L
The volume of oxygen gas at STP is 128 L.Find the number of moles.
Now the molar mass of oxygen is 32.
So 32g would ocuupy 22.4 L
128 g would occupy 128 x 22.4 /32
=4 x 22.4
=89.6 L

Determining Molar Volume and the Number of Molecules of Gas

Avogadro further determined that a mole of a gas at STP contains 6.022 x 10²³ molecules.
The determination of the molar volume of 22.4 L and the number of molecules i.e. 6.022 x 10²³  and the number of molecules i.e. 6.022 x 10²³ at STP,brought out a revolution in the study of gases as well as other phases.
Let us consider an example.
Find out the number of molecules in   128g of oxygen gas at pressure 1 atm and temperature 273⁰K.
Let us find the number of moles.
Moles=Mass in g/molar mass
=128/32
=4
Now one mole of a gas contains 6.022 x 10²³
So 4 moles would contain,
4 x 6.022 x 10²³
=24.088 x 10²³ molecules.

Non Uniform Acceleration

Introduction:

Acceleration of a body is defined as the rate of change of its velocity with time. That is, Acceleration=Change in velocity / time taken. Here, the change in velocity means the difference between the final velocity and the initial velocity. A body has a non-uniform acceleration, if its velocity increases by unequal amounts in equal intervals of time or the velocity change takes place at a non-uniform rate.

Non Uniform Acceleration

Nonuniform acceleration represents the mainly common explanation of activity.

 It refers toward difference within the speed of modify in velocity.

Just locate, it way to speeding up vary through motion. This difference is able to be articulated also within expressions of location (x) otherwise time (t).

We recognize, if we are able to illustrate non-uniform quickening within one dimension, we are capable of simply expand ing the study near two or else three dimensions with composition of activity during element path. Thus, we shall detain ourselves toward the thought of non-uniform to be exact changeable speeding up in one dimension.

We shall explain nonuniform acceleration with terms of speed or else acceleration within expressions of moreover of instance, “t”, or else location, “x”.

We shall believe that the  explanation of nonuniform speeding up through convey acceleration within expressions of speed.  As a substance of information, here it is  able to be assorted potential. In addition, nonuniform acceleration might engross understanding acceleration instance or else velocity instant graphs.

Example for Nonuniform Acceleration

The velocity or speed of a car running on the road in a crowded city continuously changes due to the frequent application of brakes. At one moment the velocity increases whereas at another moment it decreases. So, when the moving body has different accelerations at different points of time during its motion, it is said to have non-uniform acceleration or variable acceleration.

Thus, a body has a nonuniform acceleration if its velocity increases by unequal amounts in equal intervals of time or the velocity change takes place at a non-uniform rate.

Use of Sound Waves

Introduction :

Sound waves are the travelling waves and longitudinal in nature. Sound waves are mechanical waves means they need a material medium for their propagation. When the sound waves travels through the medium, the pressure is exerted at the particular points so that there are two regions created: one is called compression where pressure is more and the density of the medium is more and the other is called rarefaction where the pressure is less and the density of the material is less.

Uses of Sound Waves : Different Types of Sound Waves

Audible sound waves are ranging from 20 Hertz to 20000 hertz. Sound waves having frequency less than the 20 Hertz are called the infrasonic and the sound waves having frequency more than the 20000 hertz are called ultrasonic. 

Uses of Sound Waves

(i) Geologists use the knowledge of sound waves to locate the oil reservoirs inside the earth surface.

(ii) Earthquakes can be detected by the waves travel through different kinds of rocks.

(iii) Sound waves are used in sonar, which can explore the sea bed and the entire sea.

(iv) Bats uses the sonar waves to detect the obstacles in the their path.

(v) Sound waves obey the rules of reflection so they produce echo. Echoes are used in medical fields.

(vi) Ultrasonic sound are used for examining the prenatal scanning.

(vii) Ultrasonic waves can be used to sterilize the delicate and costly instruments. In this process the instrument is suspended in the liquid and the ultrasonic waves pass through the liquid, which makes the liquid particles in the high frequency vibrations so that the surface of the instrument cleans.

(viii) Ultrasonic waves are used to detect the flaws and cracks in the metal sheets.

(ix) Sound waves are used to remove the congestion in lungs. There is a simple medical instrument called lung flute, which break up mucus in the chest cavity.

(x) Sound waves escaping from the Sun’s interior surface create lot of hot gases, which powers the chromospheres.

(xi) Ultrasonic waves are used in the diagnostic sonography, in which we can detect the body structures and the internal organs of the human body. We can detect the tumors by use of the ultrasonic waves.

I like to share this Sound Wave Energy with you all through my blog.

Check my best blog States of Matter.

States of Matter

A state of a substance or matter describes its physical phase and composition. Matter exist in many states but there are three elementary states of matter which we see in our daily life. Let us see what are the three states of matter and examples of the three states of matter through our daily experiences.

Three basic states are: solid, liquid, and gas.

In solid state the particles of matter are closely packed. There is no free movement in the particles of the matter but there can be vibration in them. This is because the internal force of attraction between the particles is very strong. Solids have a fixed shape and volume. These cannot be changed without external pressure or force on them. Examples of these are rocks, ice, wood, sand, iron rod, paper etc.

Liquid is another phase in which a matter exists. An important property of this is that it has a constant volume but its shape is not fixed as it takes the shape of the container in which it is kept. Because of this it is in compressible fluid. In liquid states of matter molecules can move w.r.to each other and the force of attraction in them is lesser than solids. Examples: water, oil, honey, lemonade, juices, petrol etc.

Gas is the third elementary form in which matter exists. Gaseous molecules have large kinetic energy and can move freely. Gaseous matter does not have fixed volume and shape. Its volume can be increased or decreased with pressure. Inter molecular forces among them are very small. It takes the whole volume of the container in which it is kept. Eg: air, steam, oxygen, co₂ etc.

You may sometimes listen to a fourth state of matter. what are the 4 states of matter ? we have seen three elementary states yet, now the fourth state of matter is plasma. This state does not have fixed volume and shape. It is mostly found in ionized from of gas. Plasma is electrically conductive while gas is not. Eg: stars, lightning, etc.

There are seven states of matter till now which have been found. These are: above stated four states, Quark-gluon plasma, Bose-Einstein condensate and Fermionic condensate.

Quark gluon plasma particles move in one direction while in other states particles move in random directions.

Bose Einstein condensates exist when matter is frozen to very low temperature. The atoms of this state overlap on each other. Example-super-fluids and super conductors.

Fermionic condensates are obtained from fermions. This state is related to previous state. These exist in super fluid state.

Check my best blog Momentum Vector.

Momentum Vector

Introduction:

Measurement of motion of a body can be explained by momentum vector.

Definition of momentum vector:

Momentum vector is defined as the total motion contained in the body. Mathematically, momentum vector is equal to the product of mass of the body and its velocity.
P = m × v
Where m is the mass of the body and v be the velocity of the body.
Momentum vector is a vector quantity. The unit of momentum vector is kg m /s in MKS and g cm /s in CGS.

Principle of Conservation of Momentum Vector:

It states that if no external force is applied on a system, then the momentum of the system remains constant. In other words, if there is no external force applied on the system,
the initial momentum of the system will be equal to the final momentum of the system Consider a system of two bodies on which there is no external force acting on it. Because the system is isolated from the surroundings, so it interacts only due to their mutual interactions. Due to the mutual interaction, the momentum of the individual bodies may change but the total momentum of the system remains constant. If q₁ and q₂ be their individual momentum's, then
q₁ + q₂ = constant
For a system of n bodies, we can say that, q₁ + q₂ + q₃ +…..+ q_n = constant

Practical Application of Principle of Conservation of Momentum Vector:

When a bullet is fired from the gun, the gun recoils or gives a jerk in the shoulder in the backward direction. Let M be the mass of gun and m be the mass of the bullet. Initially both bullet and the gun are at rest. On firing the gun, suppose that the bullet moves with velocity v and the gun moves with velocity V. As we use the principle of conservation of momentum,
Total momentum of the gun and the bullet before firing = total momentum of the
         bullet and the gun after firing
0 = MV + mv
V = - mv / M
The negative sign shows that the gun will move in the opposite direction of bullet.

Angular Momentum for Rigid Body

Introduction:

The angular momentum definition of a particle is defined as the moment of linear momentum of the particle.
Let us consider a system of n particles of masses m₁,m₂,m₃..............m_n situated at distances of r₁,r₂,r₃,.......,r_n respectively from the axis of rotation .

Let v₁,v₂,v₃, ....be the linear velocities of the particles respectively, then the linear momentum of the first particle = m₁v₁

Definition of Angular Momentum for Rigid Body:

Since v₁ = r₁`omega`
Linear momentum of the first particle =m₁(r₁`omega` )
The moment of linear momentum of first particle = (m₁r₁`omega` )x r₁
Angular momentum of first particle = m₁r₁²`omega`
Similarly angular momentum of the second particle = m₂r₂²`omega`
and angular momentum of the third particle = m₃r₃²`omega` and so on.
The sum of moment of the linear momenta of all the particles of a rotating rigid body taken together about the axis of rotation is known as angular momentum of a rigid body.

Calculating the Angular Momentum for Rigid Body:

`:.` Angular momentum if the rotating rigid body = sum of the angular momenta of all the particles
`rArr` L = m₁r₁²`omega` +m₂r₂²`omega` +m₃r₃²`omega` +.............+m_nr_n²`omega`
`rArr` L = `omega` [ m₁r₁² +m₂r₂²+m₃r₃²+.....+m_nr_n²]
         =`omega[ sum_(i=1)^n m_i r_i^2]`
`rArr` L = `omega` I
where I = `sum_(i=1)^n m_ir_i^2` = moment of inertia of the rotating rigid body about the axis of rotation.

Problem to find the angular momentum of a cylinder:
A solid cylinder of mass 200kg rotates about its axis with angular speed 100 s^-1  .The radius of the cylinder is 0.25m.What is the magnitude of the angular momentum of the cylinder about its axis?
Given data : Mass M = 200 kgs
Angular speed `omega` =100 s^-1
Radius R=0.25m
L= ?
Formulas : I = `(MR^2)/2`
L = I`omega`
Working: I = `(MR^2)/2= (200 xx (0.25)^2)/2 = 6.25 "kg" m^2`
L = I`omega` = 6.25 x 100 = 625 Kg m² s^-1

Check my best blog Atomic Number of Curium.

Atomic Number of Curium

Curium is a silvery metal that is hard and brittle and tarnishes gradually in air at room temperature.

Introduction to atomic number of curium

It is first produced by Glenn T. Seaborg, Albert Ghiorso, and Ralph A. James at University of California in 1944. Its symbol is Cm and the atomic number of curium is 96. Curium does not occur in nature and is a synthetic chemical (produced artificially) produced in nuclear reactors by bombarding plutonium with helium ions (alpha particles).

Properties of Curium

• Molecular Weight: 247.070347 [g/mol]
• IUPAC Name: curium
• Canonical SMILES: [Cm]
• InChI: InChI=1S/Cm
• InChIKey: NIWWFAAXEMMFMS-UHFFFAOYSA-N
• Atomic number of curium: 96
• Element category: actinide
• Period and block: 7, f
• Electron configuration: [Rn]7s25f76d1
• Phase: solid
• Density: 13.51 g•cm−3
• Melting point: 1613 K
• Boiling point: 3383 K
• Crystal structure: hexagonal close-packed
• Atomic Radius: 170 pm
• Oxidation States: 3

Uses of Curium

• Curium is available only in extremely small quantities. Curium can be used as source of thermoelectric power in crewless space probes and satellites without any heavy shielding.
• Curium-242 isotope is used in radio isotopic power generators as it produces around 3 watts of heat energy per gram (through radioactive decay).
• Curium-242 is used as source of alpha particles in lunar missions to bombard alpha particles to the moon’s soil to determine materials present in moon soil.

Isotopes of Curium

About sixteen different isotopes of curium are present and some of the main isotopes are Cm-242, with half life of 160 days, Cm-243, with half life of 29 yr, Cm-244, with half life of 18 yr, Cm-245, with half life of 8,500 yr, Cm-246, with half life of 4,700 yr, Cm-247, with half life of 16 million yr, Pu-243, with half life of 5.0 hr, Cm-248, with half life of 340,000 yr, Cm-250, with half life of 6,900 yr, Pu-246, with half life of 11 days, Bk-250, with half life of 3.2 hr, and Am-246, with half life of 39 min.