MODELING REAL LIFE The pH value for a substance measures how acidic or alkaline the substance is. It is given by the formula pH \( =-\log \left[\mathrm{H}^{+}\right] \), where \( [\mathrm{H}+] \) is the hydrogen lon concentration (in moles per liter). Find the pH of vinegar, which has a hydrogen ion concentration of \( [\mathrm{H}+]=10^{-3} \) moles per liter. The pH value of vinegar is

To find the pH of vinegar using the formula \( \text{pH} = -\log [\mathrm{H}^+] \), you can substitute the given hydrogen ion concentration. Here, \( [\mathrm{H}^+] = 10^{-3} \) moles per liter. Thus, \[ \text{pH} = -\log(10^{-3}) = 3. \] So, the pH value of vinegar is 3, indicating that it is quite acidic! Vinegar, often used in cooking and as a condiment, is a classic example of an acid-base solution. The acetic acid in vinegar gives it its distinctive sour flavor and low pH. Interestingly, various types of vinegar (like balsamic, white, or apple cider) will have slightly different pH values, typically ranging from 2.5 to 3.5. Condiments like these can also be used to explore culinary science by experimenting with acidity in recipes!