Specific Heat and Heat Capacity

Heat flow in a particular chemical reaction can be determined experimentally by measuring the temperature change it produces.  Calorimetry is the measurement of heat flow. The apparatus used to measure heat flow is called calorimeter. 


Specific heat and Heat capacity

We learned  from my previous post that system can either absorb heat from the surroundings or release heat to the surroundings.  The emission and absorption of heat causes an object to change the temperature.    The temperature change of an object when it absorbs or releases heat  is determined by heat capacity. Heat capacity (C) of a substance is  the amount of heat required to raise the temperature of a given quantity of a substance by 1 K (1^oC). The greater the heat capacity, the greater the heat required to produce a given rise in temperature.  The heat capacity of 1 mol of a substance is called its molar heat capacity.   The heat capacity of 1 g of a substance is called specific heat capacity. Specific heat (s) of a substance is the amount of heat required to raise the temperature of 1 g of the substance by 1 degree Celsius.  Specific  heat is an intensive property, while heat capacity is an extensive property.  The relationship between the heat capacity and specific heat is:

C = ms

where C is the heat capacity, s is the specific heat  and m is the mass of the substance in grams.  For example, the specific heat of water (s) is 4.184 J/g.^oC, what is the heat capacity of 60 g of water?

C = 60 g (4.184 J/g.^oC) = 251 J/^oC

The unit of heat capacity is J/^oC since g is cancelled out. 

The specific heat of a substance can be determined by measuring the temperature change, ∆T, of a given amount of substance in grams , when it gains or loses a specific quantity of heat, q.

Specific heat =  q/ m x ∆T

For example, 209 J is required to increase the temperature of 50 g  water  by 1 K .  What is the  specific heat of water?

Specific Heat = 209 J  / 50 g (1.00 K) = 4.18 J/g.K

If the specific heat and the amount of substance is given so as the change in temperature, the heat that is absorbed or released can be calculated.  Look at the equation below:

q = ms∆T

                                                                           q = C∆T

∆T is the change in temperature.  ∆T  = T_final - T_initial.   For an endothermic process q is also positive and for exothermic process the q is negative.

For example: 
A 466 g of water is heated from 8.50^oC to 74.60^oC.  Calculate the amount of heat absorbed in kJ by the water.

Solution:

                                              q = ms∆T

q  = 466 g (4.184 J/g.^oC) (74.60^oC - 8.50^oC)

                                                  = 1949.7 ^oC x 66.1 ^oC
                                                  = 128875 J x( 1kJ/1000 J) 

                                                  =  129 kJ

Enthalpy and Enthalpy of Reaction

Chemical reactions can either absorb or release heat to the surroundings.  Enthalpy is a thermodynamics quantity that is account for the heat flow in chemical changes occurring at a constant pressure.  Enthalpy denoted by the symbol H, is equal to the internal energy plus the product of pressure and volume of the system:

H = E  +   PV

where E is the internal energy of the system, P is the pressure of the system , V is the volume of the system.  Enthalpy is a state function because internal energy,  pressure, and volume are all state function.  

For any chemical process, change in enthalpy can be calculated by 

∆H  =  ∆E  +  ∆(PV)

If the change occurs at constant pressure 

∆H  =  ∆E  +   P∆V

The change in enthalpy can be calculated by the change in internal energy plus the product of pressure and the change in volume.  Since work at expansion of gas is given by w = -P ∆V, so we can substitute -w for P ∆V and q +  w for ∆E.  Thus, 

∆H =  ∆E  +  P ∆V = q_p  +   w  -  w  =  q_p

the subscript  p on the heat, q, emphasizes change in constant pressure.  The change in enthalpy therefore
∆H = q_p at constant pressure.

When ∆H is positive (q_p is positive), the system has gained heat from the surroundings and the process is endothermic.  And when the ∆H is negative, the system has released heat to the surroundings, and the process is exothermic.

Example:
Indicate the sign of the enthalpy change, ∆H, in each of the following processes:
 a.  melting of ice cubes
 b. combustion of 1 g of butane

Solution:
To answer the problem we need to identify the system and find out if heat is released or absorbed by the system.  In a) ice is the system , the ice absorbs heat from the surroundings as it melts, so q_p or ∆H is positive and the process is endothermic. In b) the system is 1 g of butane and the oxygen required to combust it.  The combustion of butane in oxygen gives off heat, so q_p or ∆H is negative and therefore the process is exothermic.

Enthalpy of Reaction

Enthalpy of reaction, ∆H, is defined as the difference between the enthalpies of the products and the enthalpies of the reactants.

∆H = H(products) - H(reactants)

The enthalpy of reaction can be positive or negative depending on the process of the reaction.  For an endothermic reaction, in which the system absorbs heat from the surroundings, the ∆H is positive (∆H >0).  For an exothermic process in which the system releases heat to the surroundings, ∆H is negative (∆H <0).  

Thermochemical Equation

Thermochemical equation is a balanced equation that shows the enthalpy changes and   mass relationships.  It is important to specify a balanced equation when talking about enthalpy of reaction.  For example: 

H₂O(s)  →  H₂O(l)                          ∆H = 6.01 kJ/mol

The above equation shows the melting of ice and its change in enthalpy is 6.01 kJ/mol.  The per mol in the unit for ∆H means that this is the enthalpy change per mole of the reaction, that is 1 mole of ice is converted to 1 mole of liquid water.

Below are the guidelines that are helpful when using thermochemical equations:

1.  Enthalpy is an extensive property.  The magnitude of ∆H is directly proportional to the amount of the substance consumed in the process.   Let say for example the combustion of methane:

CH₄(g)  +  2O₂(g)  →   CO₂(g)   +   2H₂O(l)                  ∆H = -890 kJ/mol

One mole of methane releases 890 kJ of heat to the surroundings, doubling the amount will cause the increase of heat twice as much, 1780 kJ.

Let us have an example:
How much heat is released  when 4.50 g of methane gas is burned in a constant-pressure  system?

Solution: 
From the equation above, the combustion of 1 mole of methane, CH₄, released 890 kJ of heat to the surroundings.  The molar mass of methane = 16 g/mol.

Heat = 4.50 g CH₄ (1 mol CH₄/16.0 g CH₄)(-890 kJ/1 mol CH₄) = -250 kJ

2.  The enthalpy change of the reaction is equal in magnitude but opposite in sign to the ∆H  for the reverse reaction.  Example, the reverse of the combustion of methane:

CO₂(g)  +  2H₂O(l)  →  CH₄(g)  +   2O₂(g)                 ∆H = +890 kJ/mol

When the reaction is reversed, the roles of the reactants and products are also reversed.  As we can see reversing the reaction, the ∆H has the same magnitude but have an opposite sign, and this time positive.

3. The enthalpy change  for a reaction depends on the state of the reactants and products.  In writing thermochemical equation we should pay attention to the phase of the reactants and products, because it will guide you the proper value of ∆H of the reaction.   Lets say for example:

2H₂O(l)   →   2H₂O(g)                    ∆H = +88 kJ/mol

The equation above shows that 2 moles of liquid water needs 88 kJ of heat in order to convert  to 2 moles of water vapor.  While the equation below:

H₂O(s)  →  H₂O(l)                          ∆H = +6.01 kJ/mol

In the above equation shows that 1 mole of ice needs 6.01 kJ of heat in order to convert ice to liquid.  Given 2 moles of ice will only need 12.02 kJ of heat.  This shows that different phases of the same substance will have different change in enthalpy.



FOR ENTHALPY AND FIRST LAW OF THERMODYNAMICS TEST QUESTIONS CLICK HERE

The First Law of Thermodynamics

From the previous post we learned that energy can be transferred back and forth between the system and the surroundings in both open system and closed system in the forms of work and heat.  Meaning energy can be transformed from one form to another, and it can be transferred from the system to the surroundings or vice versa.  This universal truth is known as the First Law of Thermodynamics, and can be summarized by the simple statement, Energy is conserved.  Energy cannot be created nor destroyed it can be converted from one form to another.  The energy that is lost in the system is gained by the surroundings and vice versa.

Internal Energy

Internal energy of the system is the sum of the kinetic energy and potential energy of all the components of the system.  Kinetic energy components consists of various types of molecular motion and the movement of electrons within molecules.  Potential energy is determined by the attractive interactions between electrons and nuclei and repulsive interaction between electrons and between nuclei in the individual molecule as well as the interaction between molecules. Internal energy here is symbolize as E, and ∆E for change in internal energy.  To calculate the change in internal energy,

∆E = E_final - E_initial

Thermodynamics quantities such as ∆E have three parts: a number and a unit that together give the magnitude and unit of the change, and a sign that give the direction.  A positive value of ∆E results when the E_final.> E _initial, which means that the system has gained energy from the surroundings.  A negative value of ∆E results when E_final <  E_initial, which means the system lost heat to its surroundings.

Relationship between ∆E to Heat and Work

In chemistry, we are concerned with the energy changes occurring in the system and not the surroundings.  Therefore the more useful form of equation of the First Law of Thermodynamics is

∆E = q  + w

        where ∆E is the change in the internal energy
                    q is the head added or liberated from the system
                    w is the work done on or by the system

The equation above says that the change in the internal energy of the system, ∆E is the sum of the heat exchange, q,  between the system and the surroundings and the work done, w, on (or by) the system.  For the sign convention for q and w are as follows:

     - q is positive for an endothermic process and negative for exothermic process
     - w is positive for the work done on the system by the surroundings and negative for work done by the system to the surroundings

Sign Convention Used  and the Relationship among q, w, and ∆E

Sign Convention for q:
q > 0 :  Heat is transferred  from the surroundings to the system

q < 0 :  Heat is transferred  from the system to the surroundings

Sign Convention for w:
 w > 0 :  Work is done by the surroundings on the system

w < 0 :  Work is done by the system on the surroundings


Sign of ∆E = q +  w
q > 0 and w > 0 :  ∆E > 0

q < 0 and w < 0 :  ∆E < 0

q > 0 and w < 0 : The sign of ∆E depends on the magnitude of q and w

q < 0 and w > 0 : The sign of ∆E depends on the magnitude of q and w


Sample Problem:
The hydrogen and oxygen in the cylinder are ignited.  As the reaction occurs, the system loses 1150 J of heat to the surroundings.  The reaction also causes the piston to rise as the hot gases expand.  The expanding gas does 480 J of work on the surroundings as it pushes against the atmosphere.  What is the change of the internal energy of the system?

Solution:

∆E = q  +  w
     = (-1150 J) + (-480 J) = -1630 J

 Both heat and work have negative sign based from the convention sign above.  This means that the system transferred 1630 J of energy to the surroundings.


Try This:
Calculate the change in the internal energy of the system for for a process in which the system absorbs  140 J of heat from the surroundings and does 85 J of work on the surroundings.

Endothermic and Exothermic Processes

Endothermic occurs when a process occurs in which the system absorbs heat.  During this process, heat flows from the surroundings to the system, such as the melting of ice.  Ice absorbs the heat from the surrounding that is why it melts.

Exothermic occurs when the system evolves heat to the surroundings.  During this process, heat flows out of the system into the surroundings,  such as the dissolution of NaOH in water.  As the NaOH pellets dissolve in water it evolves heat to the surrounding water.

State Function

State Function is the property of the system that is determined by specifying its condition or its state (in terms in temperature, pressure, location, and so forth).  The value of a state function depends only on its present conditions not on the particular history of the sample.  Because E is a state function, ∆E depends only on the initial and final states of the system, not on how the change occurs. 

Although ∆E is a state function, q and w are not.  The specific amount of heat and work produced during a change in the state of the system depend on the way in which the change is carried out.  

  

The Nature of Energy

Energy is defined as the capacity to do work. All forms of energy are capable of doing work but not all are relevant to  chemistry.  Kinetic energy, potential energy, radiant energy, thermal energy and chemical energy are the forms of energy relevant to chemistry.

Kinetic energy is the energy in motion.  The magnitude of the kinetic energy of an object depends on it mass and speed.

E = 1/2 mv²

              where  E is the kinetic energy

                         m is the mass of an object
                         v is the speed

Based from the given equation, the kinetic energy increases as the speed of an object increases. Moreover for a given speed, the kinetic energy increases with increasing mass. Like for example, a large sport-utility vehicle traveling at 55 mph has a greater kinetic energy than a small sedan traveling at the same speed, because SUV has greater mass than the sedan.

Potential energy is another form of energy which the object possesses by virtue of its position relative to other objects. Potential energy arises when there is a force operating on an object which we called the force of gravity.  Potential energy can be calculated by the formula below:

PE = mgh

          where m is the mass of an object

                    g is the acceleration due to gravity, 9.8 m/s²

                    h is the height of the object relative to some reference height

Example a rock at the top of the cliff has more potential energy and will make a bigger splash if it falls the water below than a similar rock located partway down the cliff.

Another form of energy relevant to chemistry is the chemical energy, it is a stored energy within the structural units of chemical substances; its quantity is determined by the type and arrangement of constituent atoms.  When substances participate in a chemical reaction, chemical energy is released, stored, or converted to other forms of energy.

Thermal energy is the energy related to the random motion of the atoms and  molecules. It can be calculated from the temperature measurements.  The more vigorous the motion of molecules, the hotter the higher is the thermal energy.

Radiant energy is also called solar energy.  It came from the sun and the earth's primary source of energy. It stimulates the growth of vegetation through the process known as photosynthesis and also influences the global climate patterns.


Units of Energy

The unit of energy is joule (J), in honor of the British scientist who investigated work and heat, James Joule (1882-1889).  1 J = 1 kg-m²/s².  A mass of 2 kg moving at a speed of 1m/s possesses kinetic energy of 1 joule.

E = 1/2 mv² = 1/2 (2 kg)(1 m/s)² = 1 kg-m²/s² = 1 J

Calorie (cal) is a non-SI unit of energy which is widely used in chemistry, biology and biochemistry. It was originally defined as the amount of energy  required to raise the temperature of 1 g of water  from 14.5^oC to 15.5^oC.  1 cal =4.184 J (exactly).

A related energy unit used in nutrition is the nutritional Calorie (note that this unit is capitalized)
1 Cal = 1000 cal = 1 kcal 


System and Surroundings

When analyzing energy changes, we are concern  with the well-defined parts of the universe, the system and the surroundings.  The system is the portion of the universe single out for study while the surroundings are the rest of the universe outside the system.  For example , in the reaction of hydrogen gas  and oxygen gas in a cylinder,  the system is the hydrogen and oxygen; the piston, cylinder and everything beyond them are the surroundings. 

There are three types of systems, open system, closed system and isolated system.  An open system can exchange mass and energy usually in the form of heat with its surroundings.  Closed system allows the transfer of energy (heat) but not the mass. In isolated system does not allow the transfer of energy and mass,


  

Catalysis

A catalyst is a substance that increases the rate of chemical reaction by providing an alternate reaction pathway with lower activation energy without undergoing any change in itself.  The catalyst may react to form intermediate but it is regenerated in the next step.

Let us have an example, in the laboratory oxygen can be produced through the decomposition of potassium chlorate (KClO₃):

2KClO₃(s)   →   2KCl(s)  +  3O₂(g)

                                                                                 

This reaction is very slow even if heated strongly, however mixing black manganese dioxide (MnO₂) with KClO₃ before heating causes the reaction to occur more faster. After the reaction the MnO₂ remain unchanged and the overall chemical reaction still remains the same.

 There are three general types of catalysis:  the homogeneous catalysis, heterogeneous  catalysis and enzymes catalysis.


Homogeneous Catalysis

A homogeneous catalyst is a catalyst that is present in the same phase as the reacting molecules usually liquid solution and in gas phase.  For example in the decomposition of aqueous hydrogen peroxide, H₂O₂(aq) into water and oxygen:

2H₂O₂(aq)  →   2H₂O(l)  +  O₂(g)

Without the catalyst, this reaction is extremely very slow.  One of the substances that can catalyze the reaction is the bromide ion, Br^-(aq).  The bromide ion reacts with hydrogen peroxide in acidic solution, as shown in the reaction below:

2Br^-(aq)  + H₂O₂(aq)  +   H+   →  Br₂(aq)  +   2H₂O(l)

Hydrogen peroxide will again react with Br₂(aq) forming O₂.  Therefore, the reaction is an example of a reaction having a multistep mechanism having two elementary steps.

 Br₂(aq)  +  H₂O₂(aq)   →   2Br^-(aq)   +   2H⁺(aq)   + O₂(g)

The overall reaction is shown below:

2H₂O₂(aq)   →  2H₂O(l)  +   O₂(g)

The catalyst in the reaction is the Br^-(aq), since it was left unreacted after the reaction.  Br₂ on the other hand is the intermediate since it was formed in the first step and consumed in the second step.

In general, a catalyst lowers the overall activation energy for a chemical reaction.


Heterogeneous Catalysis

A heterogeneous catalyst is a catalyst that exists in a different phase from the reacting molecules.  It is usually a solid that is combined either with liquid or gaseous reactants.  Many industrially important reactions are catalyzed by the surfaces of solids like the Haber process, the synthesis of ammonia, and the manufacture of nitric acid.

The Haber Process

 Ammonia is an important inorganic compound in the fertilizer industry, the manufacture of explosives, and much other application,  It is formed by the reaction of N₂ and H₂, and the reaction is exothermic,

N₂(g)   +   3H₂(g)  →   2NH₃(g)        ∆H^o = -92.6 kJ/mol

This reaction is very slow at room temperature and if the temperature is increased the rate also increases but it lowers the rate of the formation of NH₃(g), instead it promotes the formation of N₂(g) and H₂(g).

Fritz Haber, a German chemist, tried hundreds of compounds that will catalyze the reaction of N₂ and H₂ to form NH₃ and discovered iron plus a few percent of oxides and aluminum at about 500^oC.   This procedure is known as the Haber Process.

In heterogeneous catalysis, the surface of the solid catalyst is the site of the reaction.  In the Haber process, the dissociation of N₂ and H₂ is done on the metal surface of the catalyst.  The two reactant molecules behave very differently on the metal surface, they are highly reactive.  Studies show that H₂ dissociates into atomic hydrogen at -196^oC while N₂ molecules dissociate at about 500^oC.  The highly reactive N and H combine rapidly at high temperatures forming NH₃.

N  +  3H   →   NH₃

Manufacture of Nitric Acid

Nitric acid is also one of the inorganic compounds that has many useful uses like production of fertilizer, dyes, drugs and explosives.  This is prepared by heating ammonia and molecular oxygen in the presence of  platinum-rhodium catalyst at about 800^oC. This process is known as Ostwald process.

4NH₃(g)  +  5O₂(g)  →  4NO(g)  +  6H₂O(g)

The nitric oxide even without the catalyst oxidizes to nitrogen dioxide:

2NO(g)   +   O₂(g)  →  2NO₂(g)

 And when dissolve in water, NO₂ forms both nitrous acid and nitric acid.

2NO₂(g)   +   H₂O(l)  →  HNO₂(aq)   +   HNO₃(aq)

On heating, the nitrous acid is converted to nitric acid.

3HNO₂(aq) →  HNO₃(aq)  +  H₂O(l)  +  NO(g)

NO(g) can be recycled to produce NO₂ and the same process occurs in step 2 above.


Enzyme Catalyst

Enzymes are called biological catalysts.  Enzymes increase the rate of biological reaction by factors ranging from 10⁶ to 10¹⁸.  Enzymes are very selective in reactions that they catalyze, and some are absolutely specific, operating for only one substrate (substance) in only one reaction.  The enzyme catalyzes are usually homogeneous with the substrate and enzymes present in the same aqueous solution.  Most enzymes are large proteins with molecular weights ranging from 10,000 to about 1 million amu.