### Video Transcript

Ethane gas can be produced by the
hydrogenation of gaseous ethene. The standard entropies and
enthalpies of formation for ethene and other materials are shown in the table. The standard change in Gibbs free
energy for the hydrogenation of ethene. At 298 Kelvin is expressed per mole
of ethene reacted. Calculate, to three significant
figures, the value of Δ𝐺 standard 298 at 298 Kelvin.

Ethane is one of the simplest
hydrocarbons and one of the simplest alkanes. Hydrogenation is the addition of
hydrogen to another substance. And ethene is the simplest
alkene. We have the information we need to
construct the reaction equation. Our first reactant is the gaseous
ethene. Our second, hydrogen. And our product is gaseous
ethane. All the substances in this reaction
are gases. And the reaction is already
balanced because we only need one equivalent of dihydrogen for each double bond.

The next thing I’m going to do is
take a look at the data in the table. Standard molar entropy is the
entropy per mole of a substance on a scale where a perfect crystal at zero degrees
Kelvin has a molar entropy of zero. Here, the standard molar entropies
have been given at 298 degrees Kelvin, which is indicated by the number in the
bottom right. And the standard character in the
top right indicates that all substances are in their standard states at one bar of
pressure.

Meanwhile, the standard enthalpy of
formation is the enthalpy change due to the formation of a substance from its
elements per mole of substance with all substances in their standard states. For instance, the enthalpy of
formation of ethene is the enthalpy change per mole of ethene when formed from
carbon in its solid graphite form and hydrogen in its gaseous form.

The next step is to take the
relevant information out of the table and put it next to the relevant chemical. That’s all the information
transferred. Just be careful to ignore the data
for ethyne and monatomic hydrogen gas. Now that we’ve got all the relevant
information from the table, we can clear it away. The question has asked us to find
the standard change in Gibbs free energy for the hydrogenation of ethene at 298
Kelvin.

Gibbs free energy is the maximum
energy available from a system under constant temperature and pressure. It’s equivalent to the enthalpy of
system minus the temperature times the entropy of the system. So, a change in Gibbs free energy
is equal to the change in enthalpy minus the temperature multiplied by the change in
entropy. So, we need to work out the change
in enthalpy for this reaction and the change in entropy. The change in entropy is just equal
to the final entropy, the entropy of the products, minus the initial entropy, the
entropy of the reactants.

We want our final Δ𝐺 to be per
mole of ethene. It’s fortunate that all the other
components in this reaction are one to one with ethene. So, the combined entropy of our
products is 229.2, the combined entropy of our reactants is 219.3 plus 130.7, and
our units are joules per Kelvin per mole of ethene. So, our final value is minus 120.8
joules per Kelvin per mole of ethene. Now, we can move on to calculating
the change in enthalpy.

The enthalpy change of a reaction
is equal to the sum of the enthalpies of formation of the products minus the sum of
the enthalpies of formation of the reactants. This equation arises from Hess’s
law and the Hess’s cycle constructed by forming the reactants and products from
their constituent elements. It arises because enthalpy is
ultimately a state function, so it doesn’t matter which route you take from the
reactants to the products as long as you get there.

So, per mole of ethene, the change
in enthalpy for the formation of our products is minus 84.0 and for our reactants is
52.4 minus zero. It makes sense that the enthalpy of
formation of H2 gas is zero because that’s already its standard state. And our units are kilojoules per
mole of ethene. And the final value for enthalpy
change is minus 136.4 kilojoules per mole of ethene. Before we plug these values into
our Δ𝐺 expression, we should change the units of our entropy. The energy unit for our entropy
change is joules, so we’ll convert that to kilojoules. We can do this by multiplying by
one kilojoule per 1000 joules, giving us minus 0.1208 kilojoules per Kelvin per mole
of ethene.

Let’s have a look at these numbers
before we plug them in. The entropy change is negative,
meaning that the reaction is exothermic. Meanwhile, there is a reduction in
entropy of the reaction. This makes sense because we’re
adding two gas molecules together. You could’ve used this fact to tell
yourself that something was wrong if you got the opposite sign. Now, let moves on to the last part
of this question, substituting our values into the equation.

So, the standard change in Gibbs
free energy for the hydrogenation of ethene at 298 Kelvin is minus 136.4 minus 298
times negative 0.1208. And our units are kilojoules per
mole of ethene. Remember, this equation only works
when we use the temperature in Kelvin. Fortunately, that’s how it’s been
provided. This all evaluates to minus 100.402
kilojoules per mole of ethene, with our final answer to three significant figures of
minus 100 kilojoules per mole of ethene. This means that for each mole of
ethene reacted with hydrogen, there is a reduction in the Gibbs free energy of the
system by 100 kilojoules. Meaning that 100 kilojoules of
energy is transmitted to the surroundings, likely as heat.