Question

As eggs age, the \(\mathrm{pH}\) of the egg white increases from about 7.9 to 9.3 as the carbon dioxide diffuses out of the egg. What is the hydrogen ion concentration in an egg, if the \(\mathrm{pH}\) is 8.3?

Short answer

[H+] = 10^(-8.3) = 5.01 \times 10^{-9} \text{ M}

Step-by-step solution

Understanding pH and Hydrogen Ion Concentration

The pH of a solution is a measure of its acidity or alkalinity, on a logarithmic scale. Mathematically, pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration: pH = -log10([H+]), where [H+] is the hydrogen ion concentration in moles per liter.

Convert pH to Hydrogen Ion Concentration

To find the hydrogen ion concentration from the pH, we use the inverse of the definition of pH: [H+] = 10^(-pH). We apply this formula to find the hydrogen ion concentration for a pH of 8.3.

Calculate the Hydrogen Ion Concentration

Substituting the given pH value into the formula gives us: [H+] = 10^(-8.3). Using a calculator, we can find the hydrogen ion concentration.

Key concepts

Understanding the pH Scale

The pH scale is a critical concept in chemistry that measures the acidity or alkalinity of aqueous solutions. The scale ranges from 0 to 14, with 7 being neutral, values below 7 indicating acidity, and values above 7 indicating alkalinity. The pH of a substance is logarithmic, which means each whole number change represents a tenfold increase or decrease in acidity. For example, a solution with a pH of 4 is ten times more acidic than a pH of 5 and a hundred times more acidic than a pH of 6.

In practical terms, the pH of egg whites can exhibit how freshness affects acidity. Fresh egg whites have a pH around 7.9 and become more alkaline as they age, reaching up to 9.3 as CO2 diffuses out. It's essential to grasp this concept, as it influences many biological and chemical processes.

Acidity, Alkalinity, and Chemical Reactions

Understanding acidity and alkalinity is vital because they are opposites on the pH scale and dramatically affect chemical reactions. Acids, with a pH less than 7, can donate hydrogen ions, H+, to other substances, while alkaline or basic solutions, with a pH greater than 7, can accept hydrogen ions. This hydrogen ion exchange is fundamental to many reactions, such as those occurring during metabolism in the human body or the fermentation process in food production.

When it comes to egg whites, their increasing alkalinity over time can influence how they behave in recipes. For cooks and food scientists alike, knowing the pH can inform how egg whites will whip or how they'll react with other ingredients, like leavening agents.

The Significance of Logarithmic Relationships

Logarithmic relationships are especially important in the context of pH because the pH scale is a logarithmic one. This relationship means that pH is the exponent that tells us how many times ten should be multiplied to reach the hydrogen ion concentration. In mathematical terms,\[ \text{pH} = -\log_{10}([\text{H}^+]) \]By understanding logarithms, students can easily switch between the pH and the hydrogen ion concentration of a solution. When solving for hydrogen ion concentration, it's important to remember that a pH decrease by 1 unit multiplies the hydrogen ion concentration by 10. Hence, a small change in pH represents a significant shift in concentration, which has far-reaching implications in all aspects of chemistry from acid-base titrations to buffer solutions.

Applying Chemistry Problem Solving

In solving chemistry problems, a systematic approach is usually best. Taking our egg white problem as an example, we first need to understand the relationship between pH and hydrogen ion concentration. Then, we use the appropriate formula to convert pH to [H+]:\[ [\text{H}^+] = 10^{-\text{pH}} \]For a pH of 8.3, we find the hydrogen ion concentration as follows:\[ [\text{H}^+] = 10^{-8.3} \]This level of problem solving requires proficiency in logarithms and exponentiation. Students must practice these fundamental skills to accurately determine chemical concentrations, predict the outcomes of reactions, and essentially, understand the nuanced behavior of chemical substances under various conditions.