Explanation:
Hypokalemia results from one of three processes: poor intake, increased excretion or secretion, or intracellular shift. This patient has some degree of dehydration, the etiology which is not immediately clear from the stem. However, mild dehydration will activate the renin-angiotensin- aldosterone system and promote K secretion in the distal tubule, in an effort to reabsorb Na and assist with restoration of intravascular volume. As long as the dehydration is not so severe as to limit renal blood blow and tubular flow rates, K secretion will occur sufficiently to lower the serum K.

Addison's disease is a problem with decreased glucocorticoid activity, either from primary non-function of ACTH release, or because of ACTH resistance at the adrenal gland. Decreased effect of corticosteroid, which possesses some mineralocorticoid activity, results in decreased capacity to secrete K and reabsorb Na, often in the setting of decreased ability to secrete H+. Patients usually are hyperkalemic, often hyponatremic, and tend to have a metabolic acidosis.

Alkalemia can cause intracellular shift of K because it helps consume H+ that is pumped out of cells by the H+/K+ ATPase, thus creating a favorable situation for K+ to actively enter cells. Acidemia will of course have the opposite effect.

Diuretics will cause this patient's electrolyte disorders in several ways. First, promotion of diuresis will result in intravascular volume depletion and activation of the RAAS system and promote K secretion as well as promote H+ secretion (see below). Secondly, diuretics such as hydrochlorothiazide and furosemide increase Na delivery to the distal nephron, and increase the likelihood of K secretion, particularly when RAAS is activated.

Vomiting will result in the generation of an alkalosis two ways: First, vomiting will cause the loss of HCl, which is an acid, thus making the patient alkalotic. The kidney should normally deal with this over several hours by trying to excrete the extra bicarbonate, but if the patient is dehydrated from excessive vomiting, several forces oppose this: First, aldosterone will become activated, which as previously mentioned, increases K secretion. Aldosterone also increases NH4+ generation in the proximal tubule, which allows for H+ secretion in the distal tubule by acting as a titratable acid (NH3->NH4+), which will maintain the alkalosis. In the setting of hypokalemia, net secretion of H+ occurs as the tubule is actively trying to reclaim K (in exchange for H+) from the urine.