Video Transcript
The reaction between hydrogen bromide and sulfuric acid forms water, sulfur dioxide,
and bromine gas. Given this data in the table, what is the standard enthalpy of reaction?
It can be difficult to measure enthalpy changes for some reactions. However, we can still calculate the enthalpy change for these reactions by using
enthalpy data from other reactions. In this question, we have been asked to determine the standard enthalpy of reaction
for the reaction between hydrogen bromide and sulfuric acid. We have also been provided the standard enthalpy of formation for each reactant and
product in the reaction.
The standard enthalpy of formation is the enthalpy change when one mole of substance
is formed from its elements in their standard states under standard conditions. But how can we use the standard enthalpies of formation to calculate the standard
enthalpy for the reaction? We can use an energy cycle to indirectly calculate the standard enthalpy of
reaction.
To construct the cycle, let’s start by writing a chemical equation for the reaction
in the problem. Using the chemical formulas provided in the table, we get the chemical equation
shown. We will need to use a coefficient of two in front of hydrogen bromide and water to
balance the equation. Let’s label this equation as reaction one.
Now we need to write equations that represent the formation of the reactants and
products from their constituent elements. The elements present in both the reactants and products are hydrogen, bromine,
sulfur, and oxygen. We can start by writing H2 plus Br2 plus S plus O2. We wrote the formulas of hydrogen, bromine, and oxygen with subscripts of two because
these elements exist as diatomic molecules in their standard states. We will also need to add coefficients of two in front of hydrogen and oxygen because
in equation one, there are four hydrogen and four oxygen atoms on either side of the
equation.
Let’s now draw an arrow from these elements to the reactants of the equation. This arrow corresponds to the standard enthalpy of formation of hydrogen bromide and
sulfuric acid. And we can label this process as reaction two.
Next, we can draw an arrow from the constituent elements to the products. This arrow, which we will label as reaction three, corresponds to the standard
enthalpy of formation of water, sulfur dioxide, and bromine gas.
We have now created an alternative pathway to calculate the standard enthalpy of
reaction one by using the standard enthalpies of formation from reactions two and
three. From this, we can write an equation that shows that the enthalpy of reaction one is
equal to the enthalpy change of reaction two plus the enthalpy change of reaction
three.
However, we need to look at the direction of the arrows in the pathway. In taking the alternative pathway from reactants to products, we are actually
completing reaction two in the opposite direction and must use the negative value of
the enthalpy of reaction two.
Now we’re ready to calculate the enthalpy changes of reactions two and three. The standard enthalpy change of reaction two is found by adding together the standard
enthalpies of formation values for two moles of hydrogen bromide and one mole of
sulfuric acid.
After substituting the values from the table, we find that the enthalpy change of
reaction two is negative 886 kilojoules per mole. The enthalpy change of reaction three is equal to the sum of the standard enthalpies
of formation of two moles of water, one mole of sulfur dioxide, and one mole of
diatomic bromine. After substituting the values from the table, we find that the enthalpy change for
reaction three is negative 838 kilojoules per mole.
We can now substitute these enthalpy changes of reactions two and three into our
equation to find the enthalpy change of reaction one. After adding the values, we find that the enthalpy change of reaction one is positive
48 kilojoules per mole.
In conclusion, the standard enthalpy of reaction for the reaction between hydrogen
bromide and sulfuric acid described in the problem is positive 48 kilojoules per
mole.
