**Core Concept**
The question pertains to the paraneoplastic syndrome associated with bronchiogenic carcinoma, specifically the electrolyte abnormality. Paraneoplastic syndromes are a group of disorders caused by the immune response to a cancer, rather than by direct local effects of the tumor cells.

**Why the Correct Answer is Right**
The correct answer is related to the syndrome of inappropriate antidiuretic hormone secretion (SIADH). Bronchiogenic carcinoma can lead to the production of ADH, causing excessive water reabsorption in the kidneys, resulting in hyponatremia (low sodium levels). This is a classic paraneoplastic syndrome associated with small cell lung carcinoma, a subtype of bronchiogenic carcinoma.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because SIADH is not typically associated with hypernatremia (high sodium levels). While it can occur, it is not the most common electrolyte abnormality seen in SIADH.
**Option B:** This option is incorrect because hypercalcemia (high calcium levels) is more commonly associated with squamous cell carcinoma of the lung, another subtype of bronchiogenic carcinoma, through the production of parathyroid hormone-related protein (PTHrP).
**Option C:** This option is incorrect because acidosis (elevated blood pH) is not typically associated with bronchiogenic carcinoma. While it can occur in various clinical contexts, it is not a direct consequence of this particular paraneoplastic syndrome.
**Option D:** This option is incorrect because hyperkalemia (high potassium levels) is not a typical electrolyte abnormality associated with bronchiogenic carcinoma or SIADH.

**Clinical Pearl / High-Yield Fact**
Small cell lung carcinoma can also present with paraneoplastic syndromes such as Eaton-Lambert syndrome (a neuromuscular disorder), Cushing's syndrome, and syndrome of inappropriate antidiuretic hormone secretion (SIADH). Remembering these associations can help you differentiate between various paraneoplastic syndromes.

**Correct Answer:** A. Hyponatremia.