Law of Chemical Equilibrium or Law of mass action

Now you are quite familiar with the term Equilibrium. We know that at equilibrium the rate of forward reaction and the rate of backward reaction are equal to each other. So, the composition of reaction mixture also has a fixed value which means the reactant and product will be present in a fixed ratio. This ratio is the characteristics of that particular reaction and it is governed by the law of equilibrium.  In this post we will learn about it. I want to tell you one thing that Equilibrium is possible only in reversible reactions and not all reactions are reversible. In the coming posts we will study reversible reactions.
 
Let's take an example of a reversible reaction in which reactant ‘A’ reacts with ‘B’ to form products ‘C’ and ‘D’. Now write the balanced equation of this reaction.  

aA+ bB ↔ cC + dD

To get the equilibrium constant K_cwe have to determine the molar concentration of all species at equilibrium. And this is shown by enclosing the specie in square bracket.

K_c = [C]^c [D]^d/ [A]^a [B]^b

Equilibrium Constant Kc 

K_c is known as equilibrium constant of the reaction. And subscript c indicates that the concentrations are expressed in moles per litre (it is also termed as Molarity and shown by symbol M). 

To get the equilibrium constant K_cwe have to determine the molar concentration of all species at equilibrium. Molar concentration is shown by enclosing the species in square bracket. Let's take an example of a real reaction.

H_2(g) + I_2(g)  ↔ HI_(g)

Now write the balanced equation in which number of moles of each element on both sides of arrow becomes equal. In the above equation if we multiply 2 on right side, then both sides will have 2 moles of ‘H’ and 2 moles of ‘I’. So the balanced equation will be:

H_2(g) + I_2(g)  ↔ 2HI_(g)  -----------(1)

and K_c will be:

K_c = [HI]²/ [H] [I]

Let's find the unit of Equilibrium constant:

K_c = [moles/L]²/ [moles/L] [moles/L]
K_c = [moles/L]

Now try a different reaction. 

HI_(g)  ↔ H_2(g) + I_2(g) 

Now write the balance equation:

2HI_(g)  ↔ H_2(g) + I_2(g)  -----------(2)

And if we name K_c for this reaction is K'_c , then:

K'_c = [H] [I]/ [HI]²

Now find out the unit of K'_c

K'_c = [moles/L] [moles/L] / [moles/L]²
K'_c = 1/ [moles/L]

So, you see the Equilibrium constant has different units for different reactions. 
One more thing, did you notice that 2^nd reaction is the reverse reaction to the 1^stone? And did you find any relation between equilibrium constants of both reactions? 

K_c = 1/ K'_c

If we reverse a reaction, equilibrium constant also gets reversed for that reaction. 
And what will happen if we multiply the reaction 1? Like:

n H_2(g) + n I_2(g)  ↔ n 2HI_(g)

K"_c = [HI]²ⁿ/ [H]ⁿ [I]ⁿ
K"_c = (K_c)ⁿ

Let's try it with real data for reaction 1. Calculate K_c if at  equilibrium, concentration of H₂ is 1.4×10^-2 mol /L , I₂ is 0.12×10^-2 mol/L and HI is 2.52×10^-2 mol/L.

K_c = (2.52×10^-2)²/ ( 1.4×10^-2) ( 0.12×10^-2)
K_c = 46.4 mol/L

Let's take another data set. Calculate K_cif take initially 2.4×10^-2 M of H₂ and 1.38×10 ^-2M of I₂ and at  equilibrium concentration of H₂ becomes 1.4×10^-2 M , I₂ becomes 0.12×10^-2 M and HI is 2.52×10^-2 M.

K_c = (2.52×10^-2)²/ ( 1.4×10^-2) ( 0.12×10^-2)

K_c = 46.4mol/L

Now you have seen that initial concentration doesn't affect the equilibrium constant. Let's take another example. 

Calculate K_c if at  equilibrium concentration of H₂ is 0.77×10^-2 mol /L , I₂is 0.31×10^-2 mol/L and HI is 3.34×10^-2 mol/L.

K_c = (3.34×10^-2)²/( 0.77×10^-2)( 0.31×10^-2)
K_c = 46.4 mol/L

You might get surprised, even after changing the equilibrium concentration, equilibrium constant doesn't change. Equilibrium constant is the characteristic of a given reaction at a particular temperature. If you change the reaction temperature of the same reaction you will get a different value of K_c.

What are the other factors which affect equilibrium and equilibrium constant? In the next post we will discuss it in detail. 

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Chemical Equilibrium

Did you ever try to balance a half filled cold drink bottle horizontally on your finger? Its a difficult task because when you try to balance it, the liquid shifts to one side and the bottle gets imbalanced. But at a point when the amount of liquid on both sides becomes equal, the bottle gets balanced on your finger. This situation is known as equilibrium.  

Reaction is a very common term which we use frequently in our daily life. We will learn about it in chemistry also. When something named A reacts to B and produce a completely different thing C, this all process is known as a chemical reaction.

A + B → C

Here A and B are reactants and C is the product. In this reaction a number of molecules react with each other and a number of product molecules are formed. If you visualize it, you will see there is a pool of molecules which are moving from reactant to product side just like the liquid moves in the bottle. Bottle is the vessel in which this reaction is carried out.    

Equilibrium is that balance point at which the number of reactant molecules are equal to the number of product molecules. But it doesn't mean that equilibrium is a static condition at which reaction gets seized. Actually at equilibrium the rate of formation of product molecules is equal to the rate of break down of product molecules changing them back to reactant molecules again. That's why number of reactant molecules remain equal to the number of product molecules and it seems that reaction has been seized. 

What is Chemical Equilibrium?

When two people of equal strength arm wrestle, there comes a stage when no one could defeat the other, this is the equilibrium stage. At arm wrestling equilibrium the forces applied by both contestants are equal and opposite. Similarly, when in a chemical reaction the rate of forward reaction (forward arrow→) becomes equal to the rate of backward reaction (backward arrow ←), it attains the equilibrium stage which is depicted by two half arrows pointing in the opposite directions.  

In the last post of liquification of gases, we have observed a plateau region in the graph, where liquid CO₂ and gas CO₂ both coexist. At the middle of the plateau we get the equilibrium point. That was an example of gas-liquid equilibrium. 

Similarly, you have seen solid-water equilibrium when you place ice in water and keep them at constant temperature above zero degree. At this condition you will see there is no change in the amount of ice and water because freezing and melting both are going on at equal rate.

You may wonder why I took the example of bottle to explain equilibrium. Because it is one of the characteristics of equilibrium.  Bottle is the vessel in which reaction is carried out, in the language of chemistry bottle is the system. Equilibrium is possible only in the closed system and as the bottle is capped it becomes the closed system. When I talk about the bottle of cold drink, can you guess which equilibrium I am talking about? Here the equilibrium is set between gas dissolved in the liquid and undissolved gas. Closed system is that system which doesn't allow molecules or heat to escape. Another characteristic of equilibrium is fixed parameters like temperature and pressure. 

Let's take an example of real chemical reaction. When we take N₂ and H₂ we get NH₃. Initially N₂and H₂ get combined to form NH₃ in forward reaction. After some time the NH₃ formed by this reaction starts to decompose to N₂ and H₂ in backward reaction.  And after some time the system reaches the equilibrium, when both reactions occur in the same rate and concentrations of product and reactants become equal. If we plot a graph between concentration and time, we can visualize it happening. In one side we take reactant concentration and on the other side we take the product concentration. Reactant vs time curve represents forward reaction, while product vs time curve represents backward reaction.  You can see in the graph that we can reach at equilibrium stage by any of the curve. That means either we took N₂ and H₂ or NH₃ alone, we would reach the equilibrium by same time. 

What happens if we take out some of the product from the system or we change the temperature or pressure of the system? How will it affect the equilibrium? You can answer all these questions but for that you'll have to learn some laws of equilibrium. In the next post we will discuss these laws and learn how to use them to find answers of these questions.

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Liquification of gases

We all are familiar with the different phases of matter viz. gas, liquid and solid. You have learned that the basic difference between these phases is the strength of inter-molecular attraction between their molecules. By changing the strength of inter-molecular attraction between molecules of any phase we can transform it to another phase.  In this post we will learn how we can transform gas into liquid phase and see how the knowledge of gases and their laws helps us to make this transition.  

When one phase transforms into another phase, one intermediate phase occurs during this transition which is present in between these two phases or you can say that this third phase is a bridge between two different phases. In the transition of gas into liquid, vapour is the intermediate phase. 

What are the key changes we have to make in the molecules of gas phase to convert it into liquid phase? We have to bring them closer so they are held together by intermolecular attraction, in order to do it we have to reduce the volume. If we apply pressure we can reduce the volume of gas. Furthermore, we need to reduce temperature to slow down the speed of molecules. That means we need to find that particular temperature, pressure and volume in which we can liquefy real gas, and here Boyle’s lawhelps us.     

In the last post you have learned that, real gases follow ideal behaviour and obey Boyle’s law at higher temperature. You have seen in the graph of pV vs p where a straight line was obtained for ideal gas, which means that its volume cannot be reduced even on applying high pressure or in other words ideal gas cannot be liquefied. On the other hand, when we reduce the temperature of real gases, they deviated from the Boyle’s law. The highest temperature at which a real gas shows deviation from ideal behaviour for the first time is the temperature at which we can liquefy a real gas. This is known as critical temperature (T_c). And corresponding pressure and volume are known as critical pressure (p_c) and critical volume (V_c).

Let’s take an example of CO₂gas. At higher temperature range from 50 ͦ C to 31 ͦ C when pressure is applied it shows perfectly Ideal behaviour as expected by Boyle’s law (to learn more visit DoReal Gases Behave Ideally?). When we reduce the temperature just a bit more to 30.98 ͦ C it shows deviation from Boyle’s law on applying pressure. In the graph this deviation is clearly recognised by a sudden change in curve. At this point we get liquid CO₂ for the first time. This temperature 30.98 ͦ C is the critical temperature (T_c) of CO₂gas. At this temperature on applying pressure CO₂ gas gets compressed and transforms into liquid CO₂.

Liquification of Gas

What happens if we further reduce the temperature? CO₂ gas shows different behaviour on applying pressure at temperature below 30.98 ͦ C.

• On compressing, initially CO₂ gas remains gas till point ‘B’
• On applying still more pressure it shows deviation from Boyle's law and a little liquid CO₂ appears
• On further compression the pressure remains constant for a period (point ‘B’ to ‘C’) and we get a plateau for this phase. In this region we get vapour CO₂that means a state in which liquid and gas coexist. 
• If we further compress it, a steep rise in pressure is observed (point ‘C’ to ‘D’). As the plateau ends we start getting liquid CO₂.

All real gases show similar behaviour as CO₂. CO₂ gas represents all real gases. But every gas has a particular set of critical constants.

So what you have learnt in this post? At critical temperature (T_c) you can liquefy a gas directly into liquid phase. It means that you can skip transition phase. But if you carry out liquification at a temperature lower than critical temperature, you will get the transition phase region or two phase portion in which gas and liquid coexist.

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Do Real Gases Behave Ideally?

In the last post we have discussed the reasons behind the non-ideal behaviour of real gases. As we behave ideally in certain conditions, real gases also do. What are those conditions in which real gases behave like an Ideal gas?

As you know intermolecular forces are responsible for the non-ideal behaviour of real gases. So think about those situations in which these forces have no significance. Inter molecular forces are effective within a small range, if we increase the distance between two molecules, Inter molecular forces will diminish.    

In Boyle’s Law you have learnt that at lower pressure the volume of gas increases, which in turn increases the distance between molecules and in the larger space, volume of molecules can be neglected.  So by decreasing pressure we can beat attractive force by increasing the distance.

But still molecules are not completely free from attractive force; there are chances that they can be affected by the attractive force if any of them passes a nearby molecule. To cancel this possibility of getting caught by attractive force of nearby molecule, we have to increase the speed (or kinetic energy) of molecules and to increase their kinetic energy we have to increase temperature. At higher temperature molecules travel with higher speed and wouldn't get caught by other molecule.

That means at lower pressure and higher temperature real gases behave like an ideal gas. The temperature at which a real gas obeys Boyle’s law is called the Boyle’s temperature or Boyle’s point. Boyle’s point of gas depends on it’s nature.

Now we know how we can modify conditions to force real gases to behave ideally. Can we measure their deviation from ideal behaviour?

We know in Ideal gas equation:

 pV = nRT

pV/ nRT = 1

For an ideal gas the ratio of pV/ nRT is equal to 1. But in case of real gases this ratio deviates from unity. This ratio is defined as ‘Compressibility Factor’ and denoted as Z.

pV/ nRT = Z

When a graph is plotted between Z and pressure, we get a straight line for ideal gas. And for real gases we get different curves showing positive or negative deviation from straight line.

If we derive another equation from it, you will be able to understand the Compressibility Factor better.

pV/ nRT = Z

if we write V as V_real

p V_real / nRT = Z

From ideal gas equation we know:

pV_ideal = nRT

V_ideal = nRT/p

Now place the value of nRT/p in the above equation:

V_real / V_ideal= Z

In a graph of Z vs Pressure for ideal gas, we get a straight line at Z=1 which is parallel to the x axis. It doesn’t mean that with increase in pressure no changes occur to ideal gas, changes occur but these changes occur in such a manner that the ratio of pV/nRT remains unity.

While in case of real gases these changes occur in undisciplined way and the ratio of pV/nRT deviates from unity. Most of the real gases show a three staged curve where they have Z ≈1 at lower pressure, Z < 1 at high pressure and Z > 1 at a still higher pressure.

Stage I:  At lower pressure where Z ≈ 1 all gases show ideal behaviour. As pressure increases most of the real gases show negative deviation where Z < 1, which means V_real is less than V_ideal which signifies that the gas gets compressed more than the ideal gas at increased pressure. Here first time real gases start disobeying the Boyle’s law (p ∝ V^-1).

Stage II: As the pressure further increases, all real gases touch the straight line for an instance when they have Z= 1 and where they behave ideally since V_real is equal to V_ideal. 

Stage III: As the pressure reaches to still higher range, all real gases again deviate from ideal behaviour and show positive deviation where Z > 1. At this stage V_real is more than V_ideal that means the gases no more follow the trend of Boyle’s law of decrease in volume on increasing pressure. At this stage real gases again start disobeying the Boyle’s law (p ∝ V^-1) and it becomes impossible to compress them. 

Now you understand that why real gases obey Ideal gas equation at lower pressure and higher temperature. Does this information benefit to us? In the next post we will see how we can use it in practical life?​

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Why Do Real Gases Deviate From Ideal Behaviour?

In the last post we have discussed few postulates of Kinetic molecular theory of gases which explains the ideal behaviour of gases. Today we will try to find out where this theory went wrong and why real gases deviate from the Ideal behaviour?

We all know gases can be liquefied under pressure. You must have heard of Compressed Natural Gas (CNG) and Liquid Petroleum Gas (LPG) both are liquid form of methane gas which are stored at high pressure. If gases can be liquefied, it means there must be some forces working between them which hold them together and gas molecules also possess volume.

That means two postulates of Kinetic molecular theory of gases are wrong in which it says:

• Ideal gas molecules are so small that they occupy a negligible space
• There is no force of attraction between these molecules.

We have learnt that molecules exert pressure when they collide with the wall of container. But it is observed that at high pressure molecules come closer and the force of attraction between them starts working. When a molecule is about to collide with the wall, this force of attraction drags it back so it cannot collide with its full impact. That’s why at high pressure, pressure experienced by the walls of container is less than the expected. For this reason scientists added a correction term to the observed pressure to get the total pressure exerted by the molecules of gas.

P_Total= P_real + an²/V²

Where ‘a’ is the constant, n is the number of moles and V is the volume of the container and P_real is the observed pressure.

Forces between molecules

Like attractive force, repulsive force also comes in action at higher pressure when molecular distance decreases. This repulsive force prevents squashing of molecules so that each molecule maintains a territory. So the volume available for the motion of molecules would be less than the volume of the container because some of its space is already occupied by the molecules. That’s why we have to subtract a correction term from the volume of the container to get the actual volume.

V_remaining = V- nb

Where ‘b’ is the constant, ‘n’ is the number of moles and ‘V’ is the volume of the container.

After doing these corrections we get a new equation for real gases which are derived from ideal gas equation:

(P_real + an²/V²) (V- nb) = nRT

This equation is known as Vander waals equation and ‘a’ and ‘b’ are known as Vander waals constants and their values depend on the characteristics of gas. ‘a’ is the measure of intermolecular attractive forces of gas and it is independent of pressure and temperature.

Now you have learnt that why real gases deviate from ideal behaviour. If you remember, I have told you that molecules are like us. Molecules don't behaved ideally just like we don’t. But there may be some conditions when they are likely to behave ideally. Can you tell me what those conditions are? In the next post we will try to find out its answer.  

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Ideal Gas Equation

You have learnt different gas laws; Avogadro law, Boyle’s and Charles law. If we combine all these laws we get a new equation which is known as Ideal Gas Equation. You may think; why do we call it Ideal gas equation? I hope you will be able to get your answer by the end of this post.

Let’s discuss the Ideal Gas Equation. When we combine all the three laws we get a new equation in which P and V are proportional to the n and T. Here R is the proportionality constant and it is same for all gases. Its value depends upon the units used for the measurement of p, V and T.

In Ideal Gas Equation, product of P and V is constant for a fixed number of moles under constant Temperature. That means if we plot a graph between PV and P we would get a straight line parallel to the x axis.

Ideal Gas Equation

On the basis of these laws, Scientists developed a theory about gas molecules known as Kinetic molecular theory of gases. A list of a few qualities of Ideal gas molecules according to this theory is as follows:

• It is assumed that ideal gas molecules are so small that they occupy a negligible space, that’s why they can be compressed into very little space.
• There is no force of attraction between these molecules that’s why they can spread in all the available space.
• These molecules are always in motion and their collisions are perfectly elastic.
• When these molecules collide with the wall of the container they exert pressure on it. On increasing temperature kinetic energy of molecules also increases, that’s why pressure increases on increasing temperature.

Calculations based on Kinetic molecular theory of gases fits well with experimental data, but when scientists tried to test how far PV= nRT reproduces pressure- volume- temperature relationship of gases, they found different graphs for different gases which were not similar to the graph of Ideal Gas Equation. There is considerable deviation from the Ideal Gas Equation. Few gases show negative deviation while some shows positive deviation from the ideal behaviour. But no gas follows Ideal behaviour as described in Ideal gas equation. That’s why these gases are called real gases.

Why real gases don’t obey Avogadro law, Boyle’s and Charles law under all conditions? To understand the reason behind it we have to look again into the model of ideal gas which is proposed by Kinetic molecular theory of gases. In the next post we will try to find out where Kinetic molecule theory of gas went wrong and how we can correct it.​

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