How does impurity of distilled water vary with time in air?
Gases like oxygen and nitrogen from air are absorbed quite easily. As you pour the water to the beaker it is most likely already saturated with those gases. Other air components and contaminants (carbon dioxide, sulfur dioxide, nitrogen oxides, ammonia) will also get quickly absorbed. How fast they will contaminate your sample depends on their concentration in the air, temperature of the water, size of the container and so on. Other possible contaminants are dust particles, impurities present inside the beaker, and even glass itself (depending of its type) is slightly soluble in water. The concentration of solid impurities will usually not change very quickly. Of course, as the water evaporates, solid impurities will concentrate.