The quick answer is that cold orange juice willhave a greater pH (be much less acidic) than roomtemperature orange juice. Similarly, warmth orangejuice will have a reduced pH (be much more acidic) thanroom temperature orange juice.

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Here iswhy:Orange juice, which typically has a pHaround 3.5, is acidic due to the fact that it consists of citricacid. Citric mountain is a weak acid which means thatit does not completely dissociate in water. Thebehavior of weak acids deserve to be explained by anequilibrium constant, Ka. Generally Ka is reportedas pKa, wherein pKa = -log(Ka). The pKa because that citricacid is 3.13.

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

And thepH is given by:pH = -log

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

The vant Hoff equation(which is derived from thermodynamics) tells usthat the adjust in Ka through temperature relies onthe enthalpy the 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 also H is the enthalpy that thereaction.

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

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

First we rearrange theequation:

lnK2 = lnK1 -H/R *(1/T2-1/T1)If wepick T2 = 1C = 274K (just above thefreezing allude of water), climate 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), then theacid will not dissociate as lot when the solutionis colder. That way there will certainly not be as muchH+ existing in the solution and the pHwill be higher.

Now if we choose T2= 37C = 310K (about the temperature of the humanbody), then us 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 much less than pKa), then the acidwill dissociate an ext when the solution is warmer.That means there will be an ext H+present in the solution and the pH will certainly belower.

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

What all of thismeans because that the overall pH is that, although the doesdepend top top temperature, there will just be verysmall changes. It will not adjust by much more thanapproximately 0.04 in the temperature rangediscussed here. Assuming that the orange juicestarts with a pH that 3.5 at room temperature, itwill stay between 3.46 and also 3.54 end thetemperature selection described above.

Ofcourse, orange juice is no purely citric mountain sothese calculations because that citric mountain only provide us anestimate because that what will happen to the pH the orangejuice. The pH must follow the same trend aspredicted here, yet the numbers might not beexactly right.

Also, keep in mind the thisis no true for all acids. Even if it is the pHincreases or decreases eventually depends top top thevalue that H. If H because that the provided acid is confident asin the situation of citric acid, climate that acid willfollow the very same trend as citric acid. However, ifH is negative, then the pH will present the oppositebehavior. For these acids with an unfavorable enthalpy,pH will rise with boosting temperature anddecrease with decreasing temperature.

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