The short answer is that cold orange juice willhave a higher pH (be less acidic) than roomtemperature orange juice. Similarly, warm orangejuice will have a lower pH (be more acidic) thanroom temperature orange juice.

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Here iswhy:Orange juice, which generally has a pHaround 3.5, is acidic because it contains citricacid. Citric acid is a weak acid which means thatit does not completely dissociate in water. Thebehavior of weak acids can be described by anequilibrium constant, Ka. Usually Ka is reportedas pKa, where pKa = -log(Ka). The pKa for citricacid is 3.13.

Any weak acid, HA, when addedto water will partially dissociate into theconjugate base, A-, and H+ (or moreaccurately H3O+). Thisreaction is described by the following equilibriumequation:HA -> A- + H+.Theequilibrium constant for this equation is:Ka =/

And thepH is given by:pH = -log

Theequilibrium constant, Ka, essentially tells us howmuch of HA will dissociate and produceH+. The bigger Ka (or the smaller pKa),the more H+ the acid will produce. Inorder to figure out how the pH changes withtemperature, we need to figure out how Ka changeswith temperature.

The vant Hoff equation(which is derived from thermodynamics) tells usthat the change in Ka with temperature depends onthe enthalpy of thereaction.

lnK2 - lnK1= - H/R *(1/T2-1/T1)

Inthe above equation, K1 andK2 are the equilibrium constants, R =8.314 J/mol K is the gas constant, T1and T2 are the initial and finaltemperatures, and H is the enthalpy of thereaction.

According to the NationalInstitute of Standards (NIST), the enthalpy ofdissociating in water (called the enthalpy ofionization) for citric acid is 4.07 kJ/mol.

If we set K1 = Ka and T1= room temperature (25C or 298K), then we can pickdifferent values of T2 and see whathappens to K2. K2 will bethe equilibrium constant at temperature2.

First we rearrange theequation:

lnK2 = lnK1 -H/R *(1/T2-1/T1)If wepick T2 = 1C = 274K (just above thefreezing point of water), then wefindlnK2 = ln(0.00074) <(4070J/mol)/(8.314 J/mol K)>*<(1/274K) 1/298K)>lnK2 = -7.21- 0.144 =-7.354K2 = 0.000641pK2 =3.19

Since K2 is less than Ka(and pK2 is greater than pKa), then theacid will not dissociate as much when the solutionis colder. That means there will not be as muchH+ present in the solution and the pHwill be higher.

Now if we pick T2= 37C = 310K (about the temperature of the humanbody), then we findlnK2 = ln(0.00074) <(4070 J/mol)/(8.314 J/mol K)>*<(1/310K) 1/298K)>lnK2 = -7.21- (-0.0636) =-7.15K2 = 0.000788pK2 =3.10Since K2 is more than Ka (andpK2 is less than pKa), then the acidwill dissociate more when the solution is warmer.That means there will be more H+present in the solution and the pH will belower.

An easier, but much less accurate wayto find the pKa at a different temperature is touse the tabulated value of -0.002 pKa/T. Thismeans that for every 1C (1K) increase intemperature, the pKa of citric acid will decreaseby approximately 0.002.

What all of thismeans for the overall pH is that, although it doesdepend on temperature, there will only be verysmall changes. It will not change by more thanapproximately 0.04 in the temperature rangediscussed here. Assuming that the orange juicestarts with a pH of 3.5 at room temperature, itwill stay between 3.46 and 3.54 over thetemperature range described above.

Ofcourse, orange juice is not purely citric acid sothese calculations for citric acid only give us anestimate for what will happen to the pH of orangejuice. The pH should follow the same trend aspredicted here, but the numbers might not beexactly right.

Also, keep in mind that thisis not true for all acids. Whether the pHincreases or decreases ultimately depends on thevalue of H. If H for the given acid is positive asin the case of citric acid, then that acid willfollow the same trend as citric acid. However, ifH is negative, then the pH will show the oppositebehavior. For these acids with negative enthalpy,pH will increase with increasing temperature anddecrease with decreasing temperature.

Ifyou try to measure the pH change of orange juicewith changing temperature with a pH meter, youwill measure a much bigger change than what ispredicted here. That is because the electricalresponse of the pH meter also depends ontemperature so it is only calibrated pro 