# What is the activity of pure water?

##### 1 Answer

I assume you mean the activity

In general, we define **activity** as:

#color(blue)(a_A = chi_Agamma_A) = (chi_Agamma_AP_A^@)/(P_A^@) = color(blue)(P_A/P_A^@)# ,where:

#a_A# is theactivityof substance#A# .#gamma_A# is theactivity coefficientof substance#A# .#chi_A = n_A/(sum_(i=1)^(N) n_i)# is themol fractionof substance#A# and#n_i# is themolsof substance#i# .#P_A# is thepartial vapor pressureofsubstance#A# .#P_A^@# is thevapor pressureofpure#A# under the same conditions.#P_A = chi_Agamma_AP_A^@# is thereal-life version of Raoult's law(i.e. for nonideal solutions).

You can find a more tailored definition here, but we can cover this in general using water as an example.

Let's say we had a pure water solution of

#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"#

As a result, the mol fraction of water in water is:

#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 **the activity of water in water is**

Another way to recognize this is to realize that, *and this is a redundant description*, but **water by itself can be treated as "water in water"**, so:

#P_A/P_A^@ = 1#

since the vapor pressure of water in this pure water "solution", **not reduced by any solutes relative to** the vapor pressure of pure water,