Chemical Energetics (4) Measuring the enthalpy change of reaction (i)

Chemical Energetics (4) Measuring the enthalpy change of reaction.

I love sherbet that sweet tangy white stuff that used to come in a yellow tube with a stick of liquorice or encased in rice paper or in a long straw or even as a dib-dab!!. 

Put this stuff in your mouth and the thing fizzes and it goes cold.

What’s going on?

Well there is an endothermic reaction going on as the sherbet mixture dissolves in your saliva. 

As it dissolves in your saliva your tongue feels cold: endothermic then….

And the fizzing must be a gas given off.

That all tells us that the reaction is a neutralisation between a solid but soluble acid, in this case citric acid C₆H₈O₇ , and a solid but soluble base, in this case sodium hydrogen carbonate NaHCO₃

How can we measure the enthalpy of reaction between citric acid and sodium bicarbonate?

The best approach to get at this enthalpy change is to use a polystyrene pot as in the diagram below:

The reaction takes place in solution and the temperature changes rising if the reaction is exothermic and decreasing if the reaction is endothermic. 

The system is the reaction that takes place and the surroundings are the solution in which the reaction happens. 

We can determine the energy transferred between reaction and the solution using the simple formula

E   = m  c  ΔT

Where E is the energy transferred, m  is the mass of solution c is the specific heat capacity of the solution and ΔT the greatest temperature change during the reaction. 

If we use excess citric acid solution and add a known mass of sodium hydrogen carbonate then we can determine the energy released per mole of sodium hydrogen carbonate. 

Here are a typical set of results and a calculation of the enthalpy change:

Suppose we add 9.36g of sodium hydrogen carbonate (0.111mol) to 31.64g of a 1.46M solution of citric acid. 

The temperature change can be recorded every 15 seconds and the results plotted as a Temperature vs time graph.

The resulting plot looks like this:

You could also record this data using a temperature probe and a datalogger. 

From the graph you can determine the greatest temperature fall.

This fall is 17^oC down to 3^oC a fall of 14^oC. 

So using E  =  m c ΔT 

E =  31.64g  *   4.18 J/g/^oC  *  14^oC

E  =    1852 Joules

In the polystyrene pot there were 0.111moles of sodium bicarbonate and 0.046 mol citric acid.

This means that the citric acid is in excess.

3 moles sodium hydrogen carbonate react with one mole citric acid

Here is the equation for the reaction:

3NaHCO₃    +    H₃C₆H₅O₇  =   Na₃C₆H₅O₇   +   3CO₂  +   3H₂O

Since 3*0.046 mol = 0.148 mol sodium hydrogen carbonate are needed to react with 0.046 mol citric acid and only 0.111 mole were added, it is the citric acid that is in excess and so it is the amount of sodium hydrogen carbonate determines the values of the enthalpy change. 

Therefore, 1852 Joules were taken in from the surroundings when 0.111 mole of sodium hydrogen carbonate were neutralized. 

Scaling up to the value of energy released per mole of sodium hydrogen carbonate

ΔH  =   1852 J/mol   =   +16,684 kJ/mol

              0.111