The relationship between acid and bicarbonate is that 1 H+ neutralizes 1 bicarbonate (HCO3) molecule as represented in the following equation:
HCl + NaHCO3 --> NaCl + H2CO3
So assuming that the stomach has a pH of 3 and a volume of 100 ml (see table 1, HS = Health Subject, mean vol = 133 ml). A pH of 3 means a concentration of H+ ions of 0.001 mol/l (conc = negative log10 of the pH...10-3 mol/l). Now, assuming all the bicarbonate added makes it to the stomach, we can work out empirically how much bicarbonate it would IN THEORY take to neutralize all the acid in the stomach
The above means that for 100 ml (0.1 l) of stomach acid there is enough hydrogen ions to neutralize 0.0001 mol (n = C * V; 0.001 mol/l * 0.1 l) of HCO3. NaHCO3 has a molar mass of 84.007 g/mol. Using our very best chemistry:
Mass = number of mole * molar mass
Mass = 0.0001 mol * 84.007 g/mol
Mass = 0.0084007 grams.
Now, there's a about 5 g of baking soda in 1 teaspoon. This is a massive amount more than you see in the equation above.
So what happens to the rest?
Well, in real life, some reacts with the food during preparation, some (a lot) is lost to decomposition from heat, some isn't consumed, and last, but certainly not least; the stomach adds more acid to maintain its pH, which is essential for function of the proteolytic enzymes in the stomach.