Heat of Reaction Formula

The heat of reaction, also known as the Enthalpy of Reaction, is the difference in the enthalpy value of a chemical reaction under constant pressure. It is the thermodynamic unit of measurement used to determine the total amount of energy produced or released per mole in a reaction. As a result, the heat of a chemical reaction may be defined as the heat released into the environment or absorbed while the reaction occurs at constant pressure and temperature, and Joule (J) is the unit used to measure the total quantity of heat received or released. 

In chemical reactions, heat is mostly transferred between the reacting system and the surroundings. Before and after the chemical transformation, the amount of heat energy is the same. In other words, the heat acquired or lost in a reacting system is equivalent to the heat gained or lost in the surroundings.

What is the Heat of Reaction?

• In simple words, the heat of a reaction is the amount of energy needed to carry out the specified reaction; it is negative for exothermic reactions and positive for endothermic reactions.

• Here, for an endothermic reaction, ∆H is positive, whereas ∆H is negative for those reactions that produce heat.

• When the given reaction is carried out at constant volume, the heat required to affect the reaction is nothing but an increase in the Internal Energy(∆U) through the ∆H/∆U, which will be negative for Endothermic and positive for Exothermic reactions.

• ΔH, or the change in enthalpy, was introduced as a way to measure the energy change of a system when calculating ΔU, or the change in internal energy, became challenging due to the need to simultaneously measure both heat and work exchanged. Under constant pressure, the change in enthalpy can be determined as,

ΔH= Q

ΔH and ΔH^º_rxn

• Δ = represents the change in the enthalpy; (ΔH_products -ΔH_reactants).
• A positive value(+) that indicates the products have greater enthalpy, or that it is an endothermic reaction (heat is required).
• A negative value( -) that indicates the reactants have greater enthalpy, or that it is an exothermic reaction (heat is produced).
• º = It's signifies that the reaction is a standard enthalpy change, and occurs at a preset pressure/temperature.
• _rxn = It's symbolise that this change is the enthalpy of reaction.

Formula for Heat of Reaction

Q = m × c × ΔT

Where,

• Q = Heat of Reaction,
• m = mass of medium,
• c = specific heat capacity of the reaction medium,
• ∆T = difference in temperature of the medium.

Besides we also have another equation as,

Heat of Reaction = ΔH (products) - ΔH (reactants) 

Where,

• ΔH = change in heat value

Solved Examples

1. Calculate the heat change that occurs with ethanol combustion when a specified quantity of the substance is burned in air to increase the temperature from 28 to 42 degrees Celsius of 200 g of water, provided that water has a specific heat capacity of 4.2J/g.K.

It is given that, 
c = 4.2 Jg^-1K^-1,
m = 200 g,
ΔT = 42 – 28 ,
i.e. ΔT = 14 °C or 14 K
Here in the question, it is mentioned that a certain amount of ethanol is burned in order to raise the temperature of the water, implying that heat absorbed by water is evolved by the ethanol combustion process. The amount of heat lost in the combustion process is equal to the amount of heat gained by the water.
The amount of heat that has been changed can be determined by using formula,
Q = m × c × ΔT
Q = 200 × 4.2 × 14
Hence, Q = 11760 J

2. When sodium chloride is dissolved in 100 g of water at 25°C, the resulting solution has a temperature of 21 °C after proper stirring. If the solution's specific heat capacity is assumed to be 4.18 J / g°C, calculate the heat change during the dissolution process.

Here it is given that,
c = 4.18 J / g°C,
m = 100 g,
ΔT = 25 – 21,
i.e. ΔT = 4 K
The process results in a temperature drop, indicating that the salt dissolution tends to heat absorption from the system. Since, the heat lost by water is same as the heat absorbed by salt,
We have,
Q = m × c × ΔT
Q = 100 × 4.18 × 4
Hence, Q = 1672 J

3. When 240 grams of iron cools from 90 °Celsius to 25 °Celsius, how much heat is released? (Given: c = 0.452 J / g °C).

We have,
m = 240 g,
Specific heat capacity of Iron (c) = 0.452 J / g°C,
ΔT = Final temperature - Initial temperature = 25 - 90 = -65 °Celsius
We have the formula,
Q = m × c × ΔT
By putting given values in above equation we get,
Q = 240 × 0.452 × (-65)
hence, Q = -7051.2 J
i.e. Q = -7.05 KJ
Hence, 7.05 KJ heat is released when the process takes place.

4. With 650 KJ of energy, how much carbon can be heated from 20 degrees C to 100 °C? (Given: c = 4.184 J / g °C)

Here we are given with,
c = 4.184 J / g degrees C,
q = 650 KJ = 650000 J
ΔT = 100 - 20 = 80 Degrees Celsius
We are asked to find the Mass (m) so we have the formula,
Q = m × c × ΔT
the above equation will give us,
m = Q / (c × ΔT)
by putting given values in above equation, we will get the actual mass of carbon required,
m =  650000 / (4.184 × 80) 
m = 1941.9 g 
i.e. m = 194 kg

5. What is the specific heat capacity of 60 grams of a substance that heats up from 30°C to 40°C when 968 J of energy was added?

m = 60 g
ΔT = 40 - 30 = 10 degrees Celsius
q = 968 Joules
We have to find the Specific heat capacity ( c ) so we have the formula,
Q = m × c × ΔT
the above equation will give us,
c = Q / (m × ΔT)
by putting given values in the above equation we will get,
c = 968 / (60 × 10)
c = 1.613 J / g°C

Conclusion

In conclusion, the heat of reaction, also referred to as reaction enthalpy, represents the change in enthalpy during a specific chemical reaction at constant pressure. It serves as a thermodynamic unit to quantify the total energy, either produced or released, per mole during the reaction. This measurement is crucial for understanding energy changes in chemical processes.

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