Problem 24 - Chemistry: Principles and Reactions

Question

Milk of Magnesia has a pH of \(10.5\). (a) Calculate \(\left[\mathrm{H}^{+}\right]\). (b) Calculate the ratio of the \(\mathrm{H}^{+}\) concentration of gastric juice, \(\mathrm{pH} 1.5\), to that of Milk of Magnesia.

Step-by-Step Solution

Answer

Answer: The concentration of H+ ions in Milk of Magnesia is 3.16 × 10^{-11} M, and the concentration in gastric juice is 3.16 × 10^{-2} M. The ratio of the concentration of H+ ions of gastric juice to that of Milk of Magnesia is 1,000,000,000:1 or 10^9:1.

Step 1: Calculate the concentration of H+ ions in Milk of Magnesia

Since pH = -log[H+], we can rewrite the formula to find the concentration of H+ ions ( [H+] ): [H+] = 10^(-pH) The question gives the pH of Milk of Magnesia as 10.5, so we can plug this value into the formula: [H+] = 10^(-10.5) Now, calculating the concentration of H+ ions: [H+] = 3.16 × 10^{-11} M

Step 2: Calculate the concentration of H+ ions in gastric juice

Repeat the same process for gastric juice, with a given pH value of 1.5: [H+] = 10^(-1.5) Now, calculating the concentration of H+ ions in gastric juice: [H+] = 3.16 × 10^{-2} M

Step 3: Calculate the ratio of H+ concentration of gastric juice to H+ concentration of Milk of Magnesia

To calculate the ratio, divide the concentration of H+ ions in gastric juice by the concentration of H+ ions in Milk of Magnesia: Ratio = (3.16 × 10^{-2} M) / (3.16 × 10^{-11} M) The units of Molarity (M) will cancel out: Ratio = 10^9 So, the ratio of the concentration of H+ ions of gastric juice to that of Milk of Magnesia is 1,000,000,000:1 or 10^9:1.

Key Concepts

Hydrogen Ion Concentration

Understanding hydrogen ion concentration is key in pH calculations. Hydrogen ions ([H^+]) are crucial in determining the acidity or alkalinity of a solution. The pH scale, which ranges from 0 to 14, reflects this concentration:

• Lower pH values (0-6) indicate higher acidity and a higher concentration of hydrogen ions.
• Higher pH values (8-14) indicate alkalinity and a lower concentration of hydrogen ions.
• A neutral pH, like that of pure water, is 7.

Mathematically, the hydrogen ion concentration is calculated using the formula \([H^+] = 10^{- ext{pH}}\). This form illustrates that as the pH decreases, the [H^+] concentration increases exponentially.
In the provided example, the concentration of hydrogen ions in Milk of Magnesia with a pH of 10.5 is calculated as \(3.16 \times 10^{-11}\) M, showing it is a basic substance with low [H^+]. By contrast, a pH of 1.5, such as that for gastric juice, results in a much higher hydrogen ion concentration \(3.16 \times 10^{-2}\) M.

Gastric Juice Acidity

Gastric juice is a highly acidic fluid in the stomach, crucial for digestion. Its acidity is primarily due to hydrochloric acid (HCl) with a typical pH around 1.5.
Key points to remember about gastric juice include:

• The high acidity assists in breaking down food, making it easier for enzymes to process nutrients.
• The low pH of 1.5 means a high concentration of [H^+], calculated as \(3.16 \times 10^{-2}\) M.
• This acidic environment also protects the body by killing potentially harmful bacteria and pathogens that are ingested.

Gastric juice's acidic nature highlights its importance in the digestive system. Calculating hydrogen ion concentration can help us understand just how strong this acidity is compared to other substances.
This analysis aids in grasping how such acidic solutions differ from more neutral or alkaline fluids, like those found in other parts of the body or different remedies, such as antacids.

Milk of Magnesia

Milk of Magnesia is a common over-the-counter medication known for alleviating symptoms of indigestion and heartburn. Its high pH value of 10.5 indicates it is a basic (alkaline) substance.
Here are the essential features of Milk of Magnesia:

• The alkaline nature helps to neutralize stomach acid, providing relief from acid-related discomforts.
• It is primarily composed of magnesium hydroxide, which reacts with stomach acid to form water and neutral salts, thus reducing acidity.
• With a low hydrogen ion concentration of \(3.16 \times 10^{-11}\) M, it represents a stark contrast to the acidic gastric juices.

Understanding its basic properties helps us appreciate Milk of Magnesia's role as an effective antacid. It counters the high acidity of gastric juice, offering a typical 10^9:1 ratio of acidity to Milk of Magnesia, which highlights its strength in neutralizing excessive acidity in the stomach.
By bringing this knowledge into context, it becomes clearer why Milk of Magnesia is such a staple in addressing acid-related stomach issues.