Video Transcript
The group one carbonate Li2CO3
thermally decomposes to form lithium oxide and carbon dioxide. What is the enthalpy change of this
reaction if the standard enthalpy of formation of lithium carbonate is negative
1,216 kilojoules per mole and the standard enthalpy of formation of lithium oxide is
negative 596 kilojoules per mole? The standard enthalpy of formation
of carbon dioxide is negative 394 kilojoules per mole.
It can be difficult to measure
enthalpy changes for some reactions. For example, the reactions may be
too slow or potentially dangerous. However, we can still calculate the
enthalpy changes for these reactions by using enthalpy data from other
reactions. In this problem, we are given the
values of the standard enthalpy of formation of three different compounds: lithium
carbonate, or Li2CO3, lithium oxide, or Li2O, and carbon dioxide, or CO2. The standard enthalpy of formation
is the enthalpy change when one mole of substance forms from its constituent
elements in their standard states and under standard conditions.
We can use these standard enthalpy
of formation values provided. But first we will need to create a
Hess cycle to show how the formation reactions are related to the decomposition
reaction in the problem. To begin our Hess cycle, let’s
first write a balanced chemical equation for the thermal decomposition of lithium
carbonate. Lithium carbonate is a solid with
the chemical formula Li2CO3. And since we are told thermal
decomposition is taking place, we can add the symbol for heat over the reaction
arrow.
The products of the reaction are
lithium oxide and carbon dioxide. The chemical formula of lithium
oxide is Li2O because two Li1+ ions are needed to bond with one O2‒ ion to form a
neutral compound. Lithium oxide is a solid under
standard conditions. We’re probably very familiar with
the chemical formula of carbon dioxide, which is CO2, and this compound is a gas
under standard conditions. As written, this chemical equation
is already balanced. Let’s label this reaction as
reaction one.
Now, let’s write a chemical
equation to represent the formation of one mole of lithium carbonate from its
constituent elements, which are lithium, carbon, and oxygen. We’ve written these elements in
their standard states. And it’s important to note that
oxygen is diatomic. Now we can draw a reaction arrow
pointing from the elements to lithium carbonate and label this reaction as reaction
two. Of course, we need to balance the
equation, which means we need to write a coefficient of two in front of lithium and
write a coefficient of three-halves in front of oxygen gas.
Next, let’s write an equation to
represent the formation of one mole of lithium oxide and one mole of carbon
dioxide. We can draw a reaction arrow from
the elements to the products and label this reaction as reaction three. This chemical equation is already
balanced.
Now that we’ve completed creating
our Hess cycle, let’s clear some space to calculate the enthalpy change of reaction
one. According to our Hess cycle, we can
state that the enthalpy change of reaction one is equal to the negative value of the
enthalpy change of reaction two plus the enthalpy change of reaction three. The reason that we need to change
the sign of the enthalpy change of reaction two is because we need to move from the
reactants to the products along our alternative pathway. Therefore, we need to reverse
reaction number two.
Now we’re ready to substitute the
standard enthalpies of formation that were provided into our equation. The enthalpy change of reaction two
is equal to the standard enthalpy of formation of lithium carbonate, which is
negative 1,216 kilojoules per mole. The enthalpy change of reaction
three is equal to the sum of the enthalpies of formation of lithium oxide and carbon
dioxide. After simplification, we see that
the enthalpy change of reaction one equals 1,216 kilojoules per mole plus negative
990 kilojoules per mole. This gives us an answer of positive
226 kilojoules per mole.
In conclusion, the enthalpy change
for the thermal decomposition of lithium carbonate is positive 226 kilojoules per
mole.
