Part 1: Using the Library, web resources, and/or other materials, find the logarithmic formula that gives the pH of a substance. State what each variable in your equation represents.
Find the pH of an acidic substance of your choice. Using this pH, show how to find the hydrogen ion concentration, [H+], of the substance using the formula. Discuss the meaning of pH and [H+], the pH scale and why your chosen substance is acidic. Use scientific notation or enough decimal places so that your answer has at least 3 place values. For example, either use 3.44*10-6 or 0.00000344.
Part 2: Suppose that the number of cars, C, on 1st Avenue in a city over a period of time t, in months, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of cars driven on 1st Avenue can be modeled by an exponential function, C= p * at (C=p*a^t) where p is the number of cars on the road on the first day recorded. If you commuted to work each day along 1st Avenue, would you prefer that the value of "a" be between 0 and 1 or larger than 1? Explain your reasoning. Be sure to reference your sources using APA style.
Part 1: To find the logarithmic formula that gives the pH of a substance, we can use the library, web resources, or other materials. One commonly used formula is the logarithmic expression:
pH = -log[H+]
In this equation, pH represents the negative logarithm (base 10) of the hydrogen ion concentration, [H+]. The square brackets, [ ], represent concentration, so [H+] denotes the concentration of hydrogen ions.
To find the hydrogen ion concentration, [H+], from the given pH, we can rearrange the formula:
[H+] = 10^(-pH)
Now, let's calculate the hydrogen ion concentration for an acidic substance. Suppose the pH of the substance is 2.3. Plugging this value into the formula:
[H+] = 10^(-2.3)
Using a calculator, we find [H+] ≈ 0.005. In scientific notation, this can be written as [H+] ≈ 5.00 x 10^(-3). The unit of concentration for [H+] is mol/L (moles per liter).
The pH scale measures how acidic or basic a substance is. It ranges from 0 to 14, with pH 0 being the most acidic and pH 14 being the most basic. pH 7 is considered neutral. The lower the pH value, the higher the hydrogen ion concentration, indicating a stronger acid. In this case, with a pH of 2.3, the substance is acidic.
Part 2: In this scenario, we have an exponential function to model the number of cars driven on 1st Avenue, given by C = p * a^t, where C represents the number of cars, p is the initial number of cars on the first day recorded, a is the growth factor, and t is the time in months.
If we commute to work each day along 1st Avenue, we would prefer that the value of "a" be larger than 1. This is because a growth factor greater than 1 implies an increasing number of cars over time. As commuters, we would ideally want a higher number of cars on the road over time to indicate a more bustling and active area, making our commute more convenient.
APA Style Reference (for Part 2):
No sources were provided for Part 2; therefore, no APA-style reference is required. Please ensure to provide proper references for the information you use in your own work.