Question

The volume of an adult's stomach ranges from about \(50 \mathrm{~mL}\) when empty to \(1 \mathrm{~L}\) when full. If the stomach volume is \(400 \mathrm{~mL}\) and its contents have a \(\mathrm{pH}\) of 2 , how many moles of \(\mathrm{H}^{+}\) does the stomach contain? Assuming that all the \(\mathrm{H}^{+}\) comes from \(\mathrm{HCl}\), how many grams of sodium hydrogen carbonate will totally neutralize the stomach acid?

Short answer

In summary, the stomach contains 0.004 moles of H+ ions with a pH of 2 and a volume of 400 mL. To completely neutralize the stomach acid, 0.336 grams of sodium hydrogen carbonate (NaHCO3) is needed.

Step-by-step solution

Find the concentration of H+ ions using the pH value

We have the pH value of stomach acid which is 2. The formula to calculate the concentration of H+ ions from the pH value is: \[ [\mathrm{H}^{+}] = 10^{-\mathrm{pH}} \] So, \[ [\mathrm{H}^{+}] = 10^{-2} \] Thus, \[ [\mathrm{H}^{+}] = 0.01\ \mathrm{M} \]

Calculate the number of moles of H+ ions in the stomach

Now that we have the concentration of H+ ions, we can calculate the number of moles present in the stomach: \[ \text{moles} = [\mathrm{H}^{+}] \times \text{volume of stomach} \] where the volume of the stomach is given in ml = 400 ml, so we need to convert it to Liters. \[ \text{volume of stomach} = 400\ \mathrm{mL} = \frac{400}{1000}\ \mathrm{L} = 0.4\ \mathrm{L} \] Now, we can calculate the number of moles of H+ ions: \[ \text{moles} = 0.01\ \mathrm{M} \times 0.4\ \mathrm{L} = 0.004\ \mathrm{moles} \]

Find the number of moles of NaHCO3 required to neutralize H+ ions

The balanced chemical equation of the neutralization reaction between HCl and NaHCO3 is: \[ \mathrm{HCl} + \mathrm{NaHCO_3} \rightarrow \mathrm{NaCl} + \mathrm{H_2O} + \mathrm{CO_2} \] From the balanced equation, 1 mole of NaHCO3 is required to neutralize 1 mole of H+. Thus, the number of moles of NaHCO3 needed is the same as the number of moles of H+ ions, which is 0.004 moles.

Calculate the mass of NaHCO3 needed for neutralization

Now that we have the number of moles of NaHCO3 needed, we can find the mass using the molar mass of NaHCO3. The molar mass of NaHCO3 is approximately 84 g/mol. So, we can calculate the mass: \[ \text{mass} = \text{moles} \times \mathrm{Molar\ Mass} \] \[ \text{mass}_{\mathrm{NaHCO_3}} = 0.004\ \mathrm{moles} \times 84\ \frac{\mathrm{g}}{\mathrm{mol}} = 0.336\ \mathrm{g} \] To summarize, the stomach contains 0.004 moles of H+ ions, and 0.336 grams of sodium hydrogen carbonate is needed to completely neutralize the stomach acid.

Key concepts

pH and H+ ion concentration

The concept of pH is fundamental to understanding acidity and alkalinity in solutions, including stomach acid. pH is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. It is defined as the negative logarithm (base 10) of the hydrogen ion (\textsc{H+}) concentration. A low pH value corresponds to a high concentration of \textsc{H+} ions and indicates an acidic solution.For example, a pH of 2 indicates a highly acidic environment, which is typical for stomach acid. To convert pH into \textsc{H+} concentration, you use the formula:\[ [\mathrm{H}^{+}] = 10^{-\mathrm{pH}} \] This equation tells us that with a pH of 2, the concentration of \textsc{H+} ions in the stomach is\[ [\mathrm{H}^{+}] = 10^{-2} \]or 0.01 moles per liter (M). Understanding this relationship aids in determining the acidity of the stomach and the amount of antacid needed for neutralization.

moles calculation

The mole is a key unit in chemistry that quantifies the amount of a substance. One mole represents approximately \(6.022 \times 10^{23}\) entities (Avogadro's number), be it atoms, ions, or molecules. When we know the concentration of a solution in moles per liter and the volume of the solution, we can calculate the number of moles present with the formula:\[ \text{moles} = [\mathrm{H}^{+}] \times \text{volume of solution (in liters)} \]In our case, the stomach volume is 400 mL which we convert to liters as 0.4 L (since 1000 mL = 1 L). The number of moles of \(\mathrm{H}^{+}\) ions can then be easily calculated as:\[ \text{moles} = 0.01\ M \times 0.4\ L = 0.004\ moles \]This step is crucial for determining how much of a substance is needed in a reaction, and for this scenario, it tells us the amount of acidic substances in the stomach.

neutralization reaction

Neutralization is a type of chemical reaction in which an acid and a base react quantitatively with each other. In a neutralization reaction, the \textsc{H+} ions from the acid and the \textsc{OH-} ions from the base combine to form water (\textsc{H2O}), and the remaining ions form a salt. The general form of the reaction is:\[ \mathrm{Acid} + \mathrm{Base} \rightarrow \mathrm{Salt} + \mathrm{H_2O} \]For the stomach acid neutralization, the reaction involved is:\[ \mathrm{HCl} + \mathrm{NaHCO_3} \rightarrow \mathrm{NaCl} + \mathrm{H_2O} + \mathrm{CO_2} \]In this specific case, sodium hydrogen carbonate (\textsc{NaHCO3}) acts as the base and neutralizes the hydrochloric acid (\textsc{HCl}) content in the stomach. According to the reaction, one mole of \textsc{NaHCO3} is needed to neutralize one mole of \textsc{HCl}, which simplifies the calculation for the required amount of antacid.

molar mass

Molar mass, often described in units of grams per mole (g/mol), is the mass of one mole of a substance (chemical element or chemical compound). It can be calculated by summing the masses of the individual elements in the compound as indicated in the periodic table of elements. For instance, sodium hydrogen carbonate (\textsc{NaHCO3}) has a molar mass of 84 g/mol.For the calculation we need to do, the knowledge of the molar mass allows us to convert the moles of a substance into grams, which is practical and tangible. Using the formula:\[ \text{mass} = \text{moles} \times \text{molar mass} \]we determine the mass of \textsc{NaHCO3} required to neutralize the stomach acid. In the context of our example with 0.004 moles of \textsc{NaHCO3}, the mass required to neutralize the stomach acid is:\[ \text{mass}_{\mathrm{NaHCO_3}} = 0.004\ moles \times 84\ \frac{g}{mol} = 0.336\ g \]Understanding the molar mass concept is essential in stoichiometric calculations and allows for the accurate preparation of solutions and the quantification of reactions.