Chemistry Part I Chapter 5 States Of Matter

STP stands for standard temperature and pressure.

The atmospheric pressure is defined as the weight exerted by the overhead atmosphere on a unit area of surface at normal temperature. 

Liquid

Standard temperature is 273.15 K  (0°C). Standard pressure is one bar or 760 mm.

SATP stands for standard ambident temperature and pressure. In SATP conditions, the standard pressure is taken as 1 bar or 10⁵ Pa and standard temperature is taken as 298·15 K.

The unit of pressure is given as= Nm^-2
The unit of volume is given as= m³
The unit of Temperature is given as= K²
Unit of mol is givne as = mol^-1.
Thus SI unit of given quantity is given as,

R represent work done per degree per mole.

The law states that at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature. It was found that for all gases (at any given pressure), the plots of volume vs. temperature is a straight line. If this line is extended to zero volume, then it intersects the temperature axis at -273⁰C.

In other words, the volume of any gas at 273 ⁰C is zero. This is because all gases get liquefied before reaching a temperature of 273⁰C.

Hence, it can be concluded that -273 ⁰C is the lowest possible temperature

Due to the absence of attractive forces between molecules, the molecules of gases can easily separate from one another.

As the automobile moves, the temperature of the tyre increases due to friction against the road. Due to increase in temperature, the air inside it expands and pressure against the walls of the tyre increases and the tyre may burst.

According to the Boyle's law, at constant Temperature (T), a volume is inversely proportional to pressure. Such as, 

Therefore, the volume of gas will become four times its original value.

By deducting the aqueous tension at that temperature from the observed pressure of the gas. 

The Boltzmann constant k, is a physical constant relating energy at the individual particle level with temperature. It is  the gas constant R divided by the  Avogadro constant N_A.

It is the temperature at which Non-ideal gas exhibits almost ideal behaviour for a considerable range of pressure. Boyle's temperature (T_B) is related to Vander Waal’s constant a, b as follows:

'

It is given as, 

In an ideal gas, there is no attraction between the molecules of a gas. Therefore, when it expands, it does no work against the intermolecular attraction. 

A weight of 1L of gas at NTP is its density. 

It is the highest temperature at which a gas can be liquefied by increasing pressure. It is denoted by T_c.

It is the volume per mole of a gas at its critical temperature and critical pressure. It is denoted by V_c. 

Evaporation is the process of the escape of liquid molecules from its surface into the gas phase. It depends on upon the nature of liquid, temperature and surface area of the liquid.

It is the pressure exerted by the vapours of the liquid in equilibrium with the liquid at particular temperature. A liquid having weaker intermolecular interaction has lower vapour pressure.

Attractive forces between water molecules are stronger than between benzene molecules. Since the energy required to vaporisation of  the water is more than that of benzene.

Alcohol and camphor lower the surface tension of water.

This is due to the existence of surface tension. The surface tension makes water surface to behave like an elastic membrane and prevents the insects from drowning.

Surface tension and Viscosity both decrease with increase in temperature.

This is because, at high temperature, molecules have high kinetic energy and can overcome the intermolecular forces to slip fast one another between the layers.

These are the weak attractive forces existing in gases, liquids, and solids. For examples,
(i) Dispersion forces or London forces. 
(ii) Dipole- dipole interactions .
(iii) Dipole-induced dipole interactions. 
(iv) Hydrogen bond -stronger intermolecular interaction.

Iodine, ammonium chloride.

No, there is no change in the volume of a solid on slight heating.

Properties of gases:
The gaseous state is the simplest of the three physical states and shows the greatest regularity in behaviour. The chief characteristic properties of gases are:
1. A gas neither possesses a definite volume nor a definite shape.
2. All the parts of a gas or a gaseous mixture have similar composition throughout.

3. Gases can expand indefinitely to fill up all the available space.

4. The molecules or atoms of a gas are in a state of continuous zig-zag motion in all directions.

5. Two or more gases mix swiftly and easily to give a homogeneous mixture.

6. On cooling and applying pressure gases can be liquefied.

7. The gases exert pressure on the walls of the container as a result of collisions of the particles against the walls of the container.

(i) Mass: The mass of a gas can be determined by weighing the container containing the gas and then emptying the container by taking out the gas and weighing the empty container gain. The difference between the two weights gives the mass of the gas. The mass of the gas can be converted into moles by using the following relation:

The moles can be converted into number of molecules by using the relation
1 Mole = 6·023 × 10²³ molecules.

(ii) Volume: Since a gas occupies the entire space of the container available to it, the volume of the gas is the same as the volume of the container.
In S.I. units volume is measured in cubic metre (m³). 1m³ = 10³ dm³ = 10⁶ cm³

The pressure of a gas is measured with the help of an instrument called manometer. Two types of manometers are used:
(i) Open end manometer
(ii) Closed end manometer.

(i) Open end manometer. It consists of a V-shaped tube with one limb shorter than the other. It is partially filled with mercury. The mercury in the longer limb is subjected to the pressure of the gas in the vessel. Thus, the difference in the levels of mercury in the two limbs represents the difference between atmospheric pressure and gas pressure.
    
Thus, by knowing the atmospheric pressure, gas pressure can be determined.

(ii) Closed end manometer: It consists of a V-shaped tube with one limb shorter than the other. It is partially filled with mercury. The shorter limb is connected to the vessel containing,

the gas whereas the longer limb is closed. In this manometer, the downward pressure exerted by the excess height of mercury column in the closed limb is balanced by the pressure of the gas in the vessel. Since there is a nearly complete vacuum in the closed longer limb, the difference in the levels of mercury in the two limbs directly gives the pressure of the gas.

Pressure represents force per unit area. The pressure expressed in terms of height of mercury column can be converted into the units of force per unit area.
Let a mercury column h cm high and A cm² in ara of cross-section exert a downward force equal to the weight of mercury column. Therefore,  per unit area of the surface is P.

where m = mass of mercury in the column
          g = acceleration due to gravity
 But mass = density x volume
               

Where ρ and V represent density and volume of mercury respectively.

Standard atmospheric pressure. A standard pressure of one atmosphere (1 atm) is defined as the pressure exerted by a column of mercury 76 cm high at 273K (density of mercury is 13·595 g cm^–3) and at standard gravity (i.e. 9·81 cm^–2). That is,
1 atm = 76·0 cm of Hg = 760 mm of Hg = 760 torr.
The S.I. unit of pressure is pascal (Pa). It is defined as the pressure exerted when a force of 1 newton (1N) acts on a 1 m² area. Pascal is related to atmosphere or bar as
1 bar =1 atm = 1 ·0133 × 10⁵ Nm^–2
= 1 ·0133 × 10⁵ Pa = 101·33 k Pa
However, for approximate work,
1 bar 1 atm = 10² k Pa = 10⁵ Pa

It is because of the following reasons:
(i) Mercury is non-volatile at ordinary temperature, therefore, the pressure exerted by the vapours above the mercury column is very small and can be neglected.
(ii) The height of the column in a barometer is inversely proportional to the density of the liquid. Since mercury is very dense, it is best for barometer as it supports column of convenient height.

This law can be represented in three ways:
(i) Graph between P (pressure) and V (volume):

If a graph is plotted between P and V of gas at a particular temperature, a curve of the form of the regular hyperbola is obtained. This shows that volume is inversely proportional to pressure. 
(ii) Graph between P (pressure) and  : (1/volume):

If a graph is plotted between P and 
a straight line is obtained which shows that pressure and volume are inversely related to each other. 
(iii) Graph between P(pressure) and PV (Product of pressure and volume):

If a graph is plotted between P and PV, a horizontal straight line is obtained. This illustrates the relationship
PV = constant.
These curves plotted at particular temperature are known as isotherms.

Gas molecules have space in between them. When the pressure is increased, the molecules of the gas are forced  to come closer and as a result, the volume occupied by the gas decreases.

From the given data,

Substituting the values, we have
             
Since balloon bursts at 0·2 bar pressure, the volume of the balloon should be less than 11·35L.

From the given data,

According to Boyle's law,
                   

Substituting the values, we have,
   

Here,

According to Boyle's law,
                      

Substituting the values, we have,
                  

From the given data.

Substituting the values in the above equation,
    

  

Charle's law states:  Pressure remaining constant the volume of a given mass of gas increases or decreases by  volume at  for each one-degree rise or fall in temperature. 
Mathematically,
 If V₀ is the volume at 0°C, then the volume at various other temperatures can be written as:
     
But if the gas is cooled to –273°C, then its volume becomes zero.

This implies that a gas at -273°C will have zero or no volume i.e. it will cease to exist. In actual practice, all gases liquefy before this temperature is reached. Also –273°C should be the lowest possible temperature because any further cooling would lead to a volume of less than zero or negative volume which is meaningless. Therefore, this temperature (–273° C) was termed as absolute zero of temperature.
Another statement of Charle’s law:
According to Charle’s law, volume of a given mass of a gas at different temperatures is related to its volume (V₀) at 0°C as follows:
Volume at 


Dividing (1) by (2), we get,
     
 
or  
[Pressure and mass of the gas constant]
Hence Charle’s law may also be stated as Pressure remaining constant, the volume of a given mass of a gas is directly proportional to absolute temperature i.e. 
Thus, if V₁ is the initial volume of the gas at temperature T₁ (in degree kelvin) and V₂ is the final volume of the gas at temperature T₂ (in degree kelvin), keeping pressure constant, then

With a temperature of absolute zero  (i.e. –273°C) as the lowest temperature, a new scale for expressing the temperature has been developed which is called absolute scale or kelvin scale and the temperature expressed on this scale is called absolute or kelvin temperature.
In the kelvin scale, the size of the degree is kept the same as on the celsius scale but the zero is shifted to –273·15 below zero on the Celsius scale.
Thus,  –273.15° C = 0 K
or         0° C   = 273.15 K
or         t° C = (273.15 + t) K

Hence temperature on absolute or kelvin scale may be obtained by adding 273.15 to the temperature on celsius scale. 
T_K = 273.15 +  t°C
In practice, the above relation is generally taken as
T_K = 273 + t° C where T is the temperature on kelvin scale and t is the temperature on celsius scale.

From the given data,

According to Charles' law
                     
    
Putting the values in the above equation,
                             
   

From the given data,

According to Charle's law,
                      
or                
Substituting the values,  we have
          
                    

From the given data,

According to Charle's law
       
 
Substituting the values,
               
   

Let the volume of vessel  = V cm³

Substituting the values, we have
     
                                     

Since the gas is confirmed in a cylinder, its volume will remain constant. 
From the given data,
 
Applying pressure temperature law,
 
 
Substituting the values in the above equation,
 

Hence the cylinder will at 

Avogadro’s law states: Equal volumes of all gases at the same temperature and pressure contain the same number of molecules.
For example, 22·4 litres of any gas at STP (273K and 760mm Hg) contain Avogadro number, N₀ (6·02×10²³) of molecules irrespective of its nature.
It follows that volume of gas V is directly proportional to N, the number of molecules at constant temperature and pressure.
V ∝ N (at constant temperature and pressure)
Also number of moles of a gas (n) ∝ number of molecules (N)

Hence the volume of gases at constant temperature and pressure is directly proportional to their number of moles.

The number of molecules of a gas is proportional to the number of moles.
  Let the mass of each gas in the two flasks be =  mg
   Molecular mass of H₂ = 2
    Molecular mass of CH₄ =16

Thus, the number of molecules of H₂ in the flask. A will be eight times the number of molecules of CH₄ in flask B.

Derivation of the ideal gas equation: Let the volume of a given mass of a gas change from V₁ to V₂ when the pressure is changed from Pi to P₂ and temperature is changed from T₁ to T₂. Suppose this change from initial state (P₁ V₁T₁) to final state (P₂V₂T₂) occurs in two steps:
First step: Suppose the volume of the given mass of the gas changes from V₁ to V_x when pressure is changed from P₁ to P₂, keeping temperature T₁ constant.

Second step: Now let the volume changed from V_x to V₂ when the temperature is changed from T₁ to T₂, keeping pressure P₂ constant.
     According to Charle's law,
                      

From (1) and (2), we have
              

The numerical value of the constant K is independent of the nature of the gas but depends on upon the amount of the gas. But at constant temperature and pressure the volume of a gas is proportional to the number of moles (n), this means that K is directly proportional to the number of moles (n).

where R is a constant of proportionality which is independent of nature as well as the amount of the gas and is known as a universal gas constant. From (4) and (5)
  
Equation (6) is known as an ideal gas equation. Alternative derivation of ideal gas equation
: According to Boyle’s law,
                
According to Charle's law,
 
 
According to Avogadro's law,
 
 
Combining (1), (2) and (3), we have,
             
.
                                  

The ideal gas equation is
              PV = nRT
     
 R represents energy or work done per degree per mole. 

The units of the gas constant (or numerical value) R in different scales of measurement may be calculated as follows:

1. In SI units:
One mole of a gas under standard conditions of temperature and pressure (STP or NTP) occupies a volume of 22·7L.

           

2. Under NTP condition (for one mole of the gas):One mole of any gas at 0°C (i.e. 273·15K.) and under 1 bar pressure occupies 22.7 L
    
According to ideal gas equation,
                    PV = nRT

Substituting the values, we have,
               

The equation of state is given by,
pV = nRT …. (i)

Where, p → Pressure of gas

V → Volume of gas

n→ Number of moles of gas

R → Gas constant

T → Temperature of gas

From equation (i) we have,

p = n RT/V

Where n= Mass of gas(m)/ Molar mass of gas(M)

Putting value of n in the equation, we have

 p = m RT/ MV ------------(ii)

Now density(ρ) = m /V ---------(iii)

Putting (iii) in (ii) we get

P = ρ RT / M

OR

ρ = PM / RT

Hence, at a given temperature, the density (ρ) of gas is proportional to its pressure (P).

Original conditions Final conditions (S.T.P.)

Applying the gas equation
              
Substituting the values, we get,
 

Original conditions:

Final conditions:
  
Applying gas equation 
Substituting the values in the above equation, we .
have,

Al reacts with caustic soda to produce dihydrogen.

 
54g Al on reacting with caustic soda produces
                                                

Applying the gas equation
        

Molecular mass of nitrogen  = 28
Number of moles of nitrogen (n)
                          

Applying ideal gas equation PV = nRT, we have,

Here mass of CO2 = 44 g mol^-1


Substituting values, we have,
 
  

Here,
n = 4.0 mol
P = 3.32 bar
V = 5 dm³,  
R = 0.083 bar dm³ K^-1 mol^-1

Applying ideal gas equation PV = nRT,

Substituting the values, we have,
          

Number of moles of methane (n₁)
                         
Number of moles of carbon dioxide (n₂)
          

We know,

At the same temperature and for same density 
           
(Gaseous oxide) (N₂)
 Here P₁ = 2 bar;    
P₂ = 5 bar;
M₂ = molecular mass of N₂ = 28
Substituting the values in equation(1), we have
      M1 x 2 = 28 x 5

Here P = 0.1 bar;

Applying general gas equation,

For gas:
                               ...(1)

Substituting the values  in eq. (1), we have,
               
For hydrogen gas:
  
 Substituting the values in eq. (1) we have,
   
    ...(3)
.
From eq. (2) and (3), we have

 
Applying ideal gas equation,    PV = nRT
Substituting the values, in the above equation, we have
  

Let the molecular masses of A and B be M_A and M_B.


Applying ideal gas equation
            PV = nRT.
For ideal gas A:
        P_AV = n_ART
For ideal gas B:
      P_BV = n_BRT

It states,“If two or more gases, which do not react chemically, are present together in an enclosed space, the total pressure exerted by the gaseous mixture is equal to the sum of partial pressures which each gas would exert if present alone in that space at the same temperature.”
Mathematically, P_total = p₁ + p₂ + p₃ + .... where P_total = total pressure exerted by the mixture in a given volume (V) at a given temperature (T)
p₁,p₂,p₃ .... = partial pressure exerted by each
gas. 
    

Here X₁, X₂ ..... are mole fractions of respective gases.
The partial pressure of a gas in a mixture is equal to the mole fraction of the gas multiplied by the total pressure exerted by the gaseous mixture.

Let the partial pressure of the gases A and B be represented by P_A and P_Brespectively.
(i) Partial pressure of gas A in 2 litre flask:
   V₁ = 300 mL;      P₂ = 600 mm
   V₂ = 2 L = 2 x 1000 = 2000 mL;  P_A = ?
According to Boyle's law,  P₁V1 = P₂V₂
i.e.  600 x 300 = PA x 2000

(ii) Partial pressure of gas B in 2 litre flask:
       V₁ = 200 mL,   P₁ = 700 mL
       V₂ = 2 litre = 2 x 1000 = 2000 mL
       P_B = ?
According to Boyle's law,
              P₁V₁ = P₂V₂
i.e.     700 x 200 = P_B X 2000

  Total pressure exerted by the mixture
      
 

Weight of oxygen  = 12 g
Molar mass of oxygen = 32g mol^-1

(a) Partial pressure of oxygen gas:
According to general gas equation,
                      PV = nRT

Substituting the value.
 
b) The partial pressure of nitrogen gas: According to the general gas equation.
                   PV = nRT
  
(c) Total pressure of the gaseous mixture : According to Dalton’s law of partial pressure,

Weight of dioxygen (O₂) = 70.6 g
Molar mass of dioxygen  = 32 g mol^-1



Mole fraction of neon
              
We know,
   Partial pressure of a gas = Mole fraction x Total pressure
         Partial pressure of  a gas  = Mole fraction x total pressure
                        = 0.21 x 25 bar = 5.25 bar
Partial pressure of neon = 0.79 x 25 bar = 19.75 bar

Partial pressure
 

Partial pressure of moisture  = 

Since the mixture H₂ and O₂ contains 20% by weight of hydrogen, therefore if H₂ = 20g, then O₂ = 100 - 20 = 80 g
   No. of moles of dihydrogen (H₂)
          
No. of moles of dioxygen (O₂) =
Partial pressure of a gas = mole fraction of the gas X total pressure,
                                

This model is used to describe the behaviour of gases. The model itself along with the assumptions regarding elastic collisions, momentum, kinetic energy, random motion, temperature, volume and pressure of gases is known as the kinetic molecular theory of gases. The main postulates of kinetic theory of gases are rapidly moving molecules. The molecules collide with one another and with the walls of the containing vessel.
Purpose: The main purpose of the kinetic theory of gases is to develop a physical picture of the nature of the gaseous state capable of explaining various laws of gaseous behaviour. This theory is applicable only to a perfect or an ideal gas.

The important assumptions/postulates of kinetic theory of gases are:
(i) A gas consists of a large number of identical molecules of mass m. The dimensions of these molecules are very-very small as compared to the space between them. Hence the molecules are treated as point masses.
(ii) The molecules of a gas are always in a state of zig-zag motion. They collide with one another and with the walls of the containing vessel. The direction of motion and speed of the molecules change continuously.
(iii) The collisions between the gas molecules are perfectly elastic i.e. there is no loss of energy during these collisions.
(iv) There are practically no attractive forces between the molecules. The molecules, therefore, move independently.
(v) The pressure of the gas is the result of collisions of molecules with the walls of the container.
(vi) The average kinetic energy of the colliding molecules is directly proportional to its absolute temperature.
In view of those assumptions, the above model of a gas is called Kinetic Gas Model or Dynamic Particle Model.

We know that molecules in a gas go on colliding with each other and hence their velocities go on changing though the average velocity remains unchanged. After the collision, the faster molecule slows down and slower molecule speeds up. The collisions are very rapid (many collisions per second) and hence, it is not possible to find the velocity of any single molecule. However, there must be a fraction of the total number of molecules that has a particular velocity at any time. The distribution of velocities amongst the gaseous molecules i.e. at a given instant how many molecules are moving with a particular speed was calculated by Maxwell and Boltzmann using the laws of probability. The fraction of molecules (∆N/N) possessing a particular velocity is taken on the Y-axis and the velocity on the X-axis. The curve obtained is shown in the figure. It is called ‘normal distribution curve of molecular velocities’.

The graph supplies the following information:
(i) The area under the curve gives the total number of molecules.
(ii) A very small fraction of molecules has very low (close to zero) velocities.
(iii) The fraction of molecules having higher and higher velocities keep on increasing with the increase in velocity, reaches a peak value and then starts decreasing for very high velocity. Once again, a very small fraction of molecules has very high velocities.
(iv) The maximum fraction of molecules possesses a velocity corresponding to the peak of the curve. This velocity is termed as most probable velocity (a). Thus, most probable velocity may be defined as the velocity possessed by the maximum fraction of molecules at a given temperature.

On increasing the temperature, the motion of the gas molecules becomes rapid and hence the value of most probable velocity also increases. As a result, the entire distribution curve becomes flatter and peak shifts to regions of higher velocities as shown in the figure.

α₁ = Most probable velocity at temp. T₁

α₂ = Most probable velocity at temp. T₂

α₂ > α₁