A Pinch Is Not a Dose: Sodium Error Bounds for Home-Mixed Oral Rehydration Solution and a Measuring Method That Holds the Band

Home-mixed sugar–salt solution is widely taught for the treatment of infant diarrhoea where oral rehydration salt packets are unavailable, typically as half a level teaspoon of salt and six level teaspoons of sugar in one litre of water, or in some teaching as pinches of salt taken by hand. This paper propagates the variability of the measures themselves — household teaspoon volume and fill, the mass of a three-finger pinch, and the volume of an unmarked household bottle — through those recipes into the resulting sodium concentration, and compares the distributions with a stated target band of 60–90 mmol/L centred on the 75 mmol/L sodium concentration of the World Health Organization reduced-osmolarity formulation. The half-teaspoon recipe fails before any variability is added: executed perfectly with a standard 5 mL teaspoon in exactly one litre it gives 51.3 mmol/L, below the band, because half a teaspoon of salt is 3.0 g against the 4.383 g per litre the target requires. Executed with real household spoons it gives a mean of 41.3 mmol/L with a standard deviation of 9.9 mmol/L, and only 4.0% of modelled batches fall inside the band; 96.0% fall below it. A six-pinch recipe gives a mean of 59.4 mmol/L with a standard deviation of 14.5 mmol/L and 40.1% in band, and a single pinch dissolved in a single glass gives a mean of 39.7 mmol/L with a standard deviation of 22.9 mmol/L and only 11.4% in band. A heaped instead of level half-teaspoon shifts the mean to 66.2 mmol/L but widens the standard deviation to 16.2 mmol/L, with 8.1% of batches above the band. Sugar shows the same pattern in miniature: a fistful delivers a mean of 35.0 g against a level-teaspoon mean of 20.4 g. The paper then originates a Cap-and-Mark method — water filled to a mark made at a known one-litre level, one level beverage-bottle cap of salt, and eight level caps of sugar — whose computed sodium distribution has a mean of 76.0 mmol/L, a standard deviation of 5.1 mmol/L, and 99.5% of batches in band. The method fails, and the paper prints those failures at full size, if a larger cap is substituted (mean 113.0 mmol/L, no batch in band), if the dose is doubled, or if a one-litre dose is mixed into half a litre (both giving a mean of about 152 mmol/L).