White wines tend to be more acidic than red wines. Find the [H3O+] concentration in a Sauvignon Blanc with a pH of 3.23 and a Cabernet Sauvignon with a pH of 3.64. How many times more acidic is the Sauvignon Blanc than the Cabernet Sauvignon?

Verified step by step guidance

Understand that pH is a measure of the acidity of a solution, defined as the negative logarithm (base 10) of the hydronium ion concentration: \( \text{pH} = -\log[\text{H}_3\text{O}^+] \).

To find the \([\text{H}_3\text{O}^+]\) concentration for the Sauvignon Blanc, use the formula \([\text{H}_3\text{O}^+] = 10^{-\text{pH}}\) and substitute the given pH value of 3.23.

Similarly, calculate the \([\text{H}_3\text{O}^+]\) concentration for the Cabernet Sauvignon using its pH value of 3.64.

To determine how many times more acidic the Sauvignon Blanc is compared to the Cabernet Sauvignon, divide the \([\text{H}_3\text{O}^+]\) concentration of the Sauvignon Blanc by that of the Cabernet Sauvignon.

Interpret the result: a higher \([\text{H}_3\text{O}^+]\) concentration indicates a more acidic solution, so the quotient from the previous step tells you how many times more acidic the Sauvignon Blanc is.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

pH Scale

The pH scale measures the acidity or basicity of a solution, ranging from 0 to 14. A pH of 7 is neutral, while values below 7 indicate acidity and above 7 indicate basicity. Each unit change in pH represents a tenfold change in hydrogen ion concentration, making it crucial for understanding the relative acidity of different solutions.

Hydronium Ion Concentration

The concentration of hydronium ions ([H3O+]) in a solution is directly related to its pH. The formula [H3O+] = 10^(-pH) allows us to calculate the hydronium ion concentration from the pH value. This concept is essential for quantifying acidity and comparing the acidity of different solutions, such as the wines in this question.

Acidity Comparison

To compare the acidity of two solutions, one can calculate the ratio of their hydronium ion concentrations. This ratio indicates how many times more acidic one solution is compared to another. In this case, by determining the [H3O+] for both wines, we can assess the relative acidity of Sauvignon Blanc and Cabernet Sauvignon.

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