Video Transcript
Using the standard enthalpies of
combustion in the table below, calculate the enthalpy change for the following
reaction: C6H5OH plus three H2 react to form C6H11OH.
It can be difficult to measure
enthalpy changes for certain reactions. For situations like this, we can
calculate enthalpy changes indirectly by using enthalpy data from other
reactions. In this question, we are being
asked to determine the enthalpy change for the reaction of phenol with diatomic
hydrogen to produce cyclohexanol. We have been provided with the
standard enthalpies of combustion for the substances involved in the chemical
reaction.
The standard enthalpy of combustion
is the enthalpy change when one mole of substance burns completely in oxygen under
standard conditions and standard states. But how can we use the standard
enthalpies of combustion provided to calculate the standard enthalpy for the
reaction in this problem? We can use a Hess cycle to help
us. Let’s clear some space to work.
Let’s begin by labeling the
reaction given in the question as reaction one. Next, we need to write an equation
for the combustion of the reactants: C6H5OH and three H2. Phenol and diatomic hydrogen will
combust in excess oxygen to produce carbon dioxide and water. However, in order to balance this
combustion equation, we need to place a coefficient of six in front of both CO2 and
H2O. Let’s label this reaction as
reaction two.
Now let’s write an equation for the
combustion of cyclohexanol. If excess oxygen is present, this
reaction also produces six moles of CO2 and six moles of H2O. Let’s label this reaction as
reaction three.
Now we have an alternative route we
can use to calculate the enthalpy of the reaction using the standard enthalpies of
combustion. We can state that the enthalpy
change of reaction one is equal to the enthalpy change of reaction two plus the
enthalpy change of reaction three. However, we should note that by
taking the alternative route, we are moving in the opposite direction to the arrow
in reaction three. Therefore, we should subtract the
enthalpy change of reaction three in our equation.
Let’s now calculate the enthalpy
change for reaction two. We can calculate the enthalpy
change of reaction two by adding together the standard enthalpy of combustion of
phenol and three times the standard enthalpy of combustion of diatomic hydrogen. We multiply the standard enthalpy
of combustion of H2 by three because there are three moles in the balanced
equation. After substituting the values from
the table into our equation, we get negative 3,051 kilojoules per mole plus three
times negative 286 kilojoules per mole. Therefore, the enthalpy change of
reaction two is negative 3,909 kilojoules per mole.
The enthalpy change of reaction
three is simply the standard enthalpy of combustion of cyclohexanol. So the enthalpy change of reaction
three is negative 3,726 kilojoules per mole.
Now let’s substitute these values
into the equation we created earlier. The enthalpy change of reaction one
equals negative 3,909 kilojoules per mole minus negative 3,726 kilojoules per
mole. After solving, the result is
negative 183 kilojoules per mole.
In conclusion, after using the
standard enthalpies of combustion provided, we find that the enthalpy change for the
reaction between phenol and diatomic hydrogen to produce cyclohexanol is negative
183 kilojoules per mole.
