Question

Gastric juice contains $3.0$ g of $HCl$ per litre. If a person produces $2.5$ litres of gastric juice per day, then how many antacid tablets each containing $400$ mg of $Al(OH{)}_3$ are needed to neutralize all the $HCl$ produced in one day?

• A. $18$
• B. $14$
• C. $20$
• D. $17$

Answer 1

Answer: (B)

$14$

$1$ litre of gastric juice contains $3$ g of $HCl$.

Therefore, $2.5$ litres of it contains $7.5$ g of $HCl$.

Number of moles of $HCl$ produced in a day = $\frac{7.5}{36.5}$ $=0.205$ moles.

Molecular weight of $HCl=36.5$ g/mol.

$6HCl+2Al(OH{)}_3\to 2AlC{l}_3+6H_{2}O$

From this reaction, we can say that $6$ moles of $HCl$ completely neutralised $2$ moles of $Al(OH{)}_3$.

Thus, $0.205$ moles of $HCl$ requires $\frac{0.205\times 2}{6}$ $=0.068$ moles of $Al(OH{)}_3$.

Now, $0.068$ moles of $Al(OH{)}_3$ correspond to $5.3$ g of $Al(OH{)}_3$ by weight.

Molecular weight of $Al(OH{)}_3$ $=78$.

$1$ antacid tablet contains $400$ mg or $0.4$ g of $Al(OH{)}_3$.

Thus, $N$ antacid tablet corresponds to $5.3$ g of $Al(OH{)}_3$.

$N$ $=13.25$

Hence, the number of antacid tablets each containing $400$ mg of $Al(OH{)}_3$ needed to neutralize all the $HCl$ produced in one day is $14$.