The short answer is the cold orange juice willhave a greater pH (be much less acidic) 보다 roomtemperature orange juice. Similarly, heat orangejuice will have actually a lower pH (be more acidic) thanroom temperature orange juice.

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Here iswhy:Orange juice, which typically has a pHaround 3.5, is acidic since it consists of citricacid. Citric mountain is a weak mountain which means thatit walk not totally dissociate in water. Thebehavior of weak acids can be defined by anequilibrium constant, Ka. Generally Ka is reportedas pKa, where pKa = -log(Ka). The pKa for citricacid is 3.13.

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

And thepH is given by:pH = -log

Theequilibrium constant, Ka, basically tells united state howmuch the HA will certainly dissociate and produceH+. The larger Ka (or the smaller sized pKa),the an ext H+ the acid will produce. Inorder to figure out just how the pH changes withtemperature, we need to number out just how Ka changeswith temperature.

The vant Hoff equation(which is acquired from thermodynamics) tells usthat the adjust in Ka with temperature counts onthe enthalpy of thereaction.

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

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

According come the NationalInstitute of requirements (NIST), the enthalpy ofdissociating in water (called the enthalpy ofionization) because that citric acid is 4.07 kJ/mol.

If we collection K1 = Ka and also T1= room temperature (25C or 298K), climate we have the right to pickdifferent values of T2 and see whathappens to K2. K2 will certainly bethe equilibrium consistent at temperature2.

First us rearrange theequation:

lnK2 = lnK1 -H/R *(1/T2-1/T1)If wepick T2 = 1C = 274K (just above thefreezing suggest 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 higher than pKa), climate theacid will certainly not dissociate as much when the solutionis colder. That method there will not be as muchH+ existing in the solution and the pHwill it is in higher.

Now if we pick T2= 37C = 310K (about the temperature the 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 an ext than Ka (andpK2 is less than pKa), then the acidwill dissociate much more when the equipment is warmer.That way there will certainly be much more H+present in the solution and also the pH will belower.

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

What all of thismeans for the all at once pH is that, although that doesdepend on temperature, there will only be verysmall changes. It will certainly not readjust by much more thanapproximately 0.04 in the temperature rangediscussed here. Assuming that the orange juicestarts v a pH of 3.5 in ~ room temperature, itwill stay between 3.46 and also 3.54 over thetemperature selection described above.

Ofcourse, orange juice is not purely citric acid sothese calculations because that citric acid only give us anestimate because that what will happen to the pH of orangejuice. The pH must follow the exact same trend aspredicted here, however the numbers could not beexactly right.

Also, store in mind the thisis not true for all acids. Even if it is the pHincreases or decreases eventually depends ~ above thevalue the H. If H for the offered acid is confident asin the instance of citric acid, climate that acid willfollow the very same trend together citric acid. However, ifH is negative, then the pH will present the oppositebehavior. For these acids with an unfavorable enthalpy,pH will boost with increasing temperature anddecrease with decreasing temperature.

Ifyou try to measure the pH adjust of orange juicewith changing temperature through a pH meter, youwill measure a lot bigger change than what ispredicted here. The is due to the fact that the electricalresponse the the pH meter additionally depends ontemperature so it is only calibrated pro