What is the activity of pure water?

Question

Ellie Andrews · Accepted Answer

I assume you mean the activity #a# of liquid water... which is just the "real life" version of concentration. Broadly speaking, activity is defined as: #color(blue)(a_A = chi_Agamma_A) = (chi_Agamma_AP_A^@)/(P_A^@) = color(blue)(P_A/P_A^@)#, where A more specific definition can be found here, but let's use water as an example to discuss this in general. Let's say we had a pure water solution of #"pH"# #7# at #25^@ "C"# and #"1 atm"#, with concentrations #["H"^(+)] = 10^(-7) "M"# and #["OH"^(-)] = 10^(-7) "M"#. In a #"1 L"# solution, we thus have: #n_(H^(+)) = 10^(-7) "mols"#
#n_(OH^(-)) = 10^(-7) "mols"#
#n_(H_2O) = cancel"1 L" xx (997.0749 cancel"g")/cancel"L" xx "1 mol water"/(18.015 cancel"g") = "55.34 mols"# The mol fraction of water in water is thus: #chi_(H_2O) = n_(H_2O)/(n_(H^(+)) + n_(OH^(-)) + n_(H_2O))# #= "55.34 mols"/(10^(-7) "mols" + 10^(-7) "mols" + "55.34 mols")# #= 0.9999999964 cdots ~~ 1# It is known that as #chi_A -> 1#, #gamma_A -> 1#. Since #chi_A ~~ 1#, it follows that #a_A ~~ 1#, and the activity of water in water is #bb1#. Another way to see this is to understand that water can be thought of as "water in water" on its own, which is a redundant description. Therefore: #P_A/P_A^@ = 1# since the vapor pressure of water in this pure water "solution", #P_A#, is (effectively) not reduced by any solutes relative to the vapor pressure of pure water, #P_A^@#, both at the same temperature and pressure.

Kai Bowman · Answer

undefined The activity of pure water is defined as 1.