# The rate of change in pH v.s Temperature

I have somewhat established that there is a linear relationship between change in pH of carbonic fizzy drinks over time. I also realise that the pH increases linearly faster for the same carbonated fizzy drink when the temperature of the drink is changed (increased).

Now the problem is, when I graph the relationship between the rate of pH increase (y-axis) and the temperature (x- axis), I get an exponentially increasing relationship. I do not know if this relationship is true, but even if it was true I do not know how to explain why this is true.

Are there any equations I can manipulate to show a mathematical relationship between rate of pH increase and temperature of the same carbonated fizzy drink?

• Check the ratio of $\mu$/kT, since pH can be defined as the chemical potential ($\mu$) divided by thermal energy (kT). Hence pH is proportional to the chemical potential due to $\ce{H+}$ concentration reduced by kT. If, for a given system, the ratio of $\mu$/kT remains constant with temperature, pH is expected to be independent of temperature. Otherwise, pH could change accordingly. – Zenix Feb 27 at 15:17
• I appreciate the help, but I am not sure how to do this as I am just doing this for a practise experiment with not so much background in chemistry... – Aurora Borealis Feb 27 at 15:36

You are dealing with temperature variation of carbonic fizzy drinks. So, the situation is somewhat tricky.

Lets approach the problem step by step.

1. If you raise temperature of neutral water, the rate of decomposition of water will increase. So, the water will contain more protons at higher temperature than at lower temperature, although the neutrality is maintained. Therefore, the pH of neutral water will decrease with temperature. pH of water at 100°C is ~6.126.

2. Carbonic fizzy drinks contain sodium & potassium bicarbonate salts, which ionize completely in aqueous solution to yield alkali cations & bicarbonate anions. The initial pH is between 3 and 4. (1)

3. Bicarbonate anion can capture a proton from the system to yield carbonic acid. Carbonic acid is unstable and thus decomposes even at room temperature to produce carbon-dioxide, & thus the bubble! So, even at room temperature gradually the solution turns less acidic, then neutral & finally alkaline. So, here you are not increasing temperature & just letting time to flow, & the pH rises gradually. Therefore, I can expect 'linear relationship between change in pH of carbonic fizzy drinks over time'.

4. When you raise temperature of carbonic fizzy drinks, the pH increase gets faster because the decomposition of carbonic acid is very much temperature sensitive. It is worthwhile to mention that the rapid pH rise is somewhat countered by the pH lowering due to water's decomposition, but that effect is much less significant as water's decomposition is much less sensitive to temperature. In this case, I can certainly expect deviation from linear behavior (nonlinear or exponential increase) aided by temperature influenced decomposition of carbonic acid.

You may be able to arrive at a mathematical relationship by combining the temperature dependency of carbonic acid & water decomposition.

• I somehow amended it. Please check. – Sujay Ghosh Feb 27 at 17:21
• I appreciate the feedback, however I do not know exactly how to arrive at a mathematical derivation even though experimentally it seems to show a non linear behaviour as you also mentioned.. – Aurora Borealis Feb 29 at 9:47
• To draw a plot it is important to know the initial composition of the carbonic fizzy drink. It usually contains sodium chloride, sodium citrate, sodium bicarbonate, potassium bicarbonate, potassium citrate, potassium sulfate, or disodium phosphate, depending on the product. pH is increasing due to the presence of $Na^+$ & $K^+$ which were added as biocarbonates. After complete decomposition of carbonic acids, charges of those $Na^+$ & $K^+$ ions will be balanced by $OH^-$ ions, and hence you can measure the final pH value. – Sujay Ghosh Feb 29 at 14:09
• Now you need to determine the initial concentration of carbonic acid. Remember that carbonic acid is a weak acid, and its concentration is linked with the initial concentration of $HCO_3^-$ through the equilibrium constant. Then find the rate of decomposition of carbonic acid, and how that rate increases with rise of temperature. – Sujay Ghosh Feb 29 at 14:09