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, you need to understand the concept of pH and the properties of acids and bases. The pH scale is a measure of acidic or basic (alkaline) characteristics of a substance. It ranges from 0 to 14, where values below 7 are acidic, 7 is neutral, and values above 7 are basic. The formula to calculate pH is given by:
pH = -log[H+]
In this equation, [H+] represents the concentration of hydrogen ions in the substance. The negative logarithm of [H+] is taken to obtain a convenient scale for measuring the acidity or basicity.
To find the hydrogen ion concentration, [H+], using the pH value, you can rearrange the equation:
[H+] = 10^(-pH)
In this formula, the pH value is substituted into the equation, and 10 is raised to the power of negative pH to calculate the concentration of hydrogen ions.
Now, let's find the pH of an acidic substance and demonstrate how to find the hydrogen ion concentration:
Let's say the pH of the substance is 3.5.
Using the formula [H+] = 10^(-pH):
[H+] = 10^(-3.5) = 0.000316227 (in scientific notation) or 0.000316 (rounded to three decimal places)
The meaning of pH is a measure of the acidity or alkalinity of a substance. A lower pH value indicates a higher concentration of hydrogen ions and therefore a higher acidity. An acidic substance has a higher concentration of hydrogen ions than hydroxide ions (OH-).
The hydrogen ion concentration, [H+], represents the amount of hydronium (H3O+) ions present in the substance. It is a measure of the relative acidity or basicity of a solution.
The chosen substance is acidic because its pH value is less than 7. The pH scale classifies substances with a pH below 7 as acidic. The specific substance chosen to determine its pH and [H+] was not stated, so the example values provided above are general in nature.
Part 2:
To determine whether you would prefer the value of "a" in the exponential function C = p * a^t to be between 0 and 1 or larger than 1 for commuting to work along 1st Avenue, you need to understand the behavior of exponential functions.
If a value of "a" in the equation is between 0 and 1, it represents a decay or decrease over time. This means that the number of cars on 1st Avenue would decrease as time progresses, which may not be ideal for commuting.
On the other hand, if the value of "a" is larger than 1, it represents growth or increase over time. This means that the number of cars on 1st Avenue would increase as time progresses, which could lead to congestion and longer commute times.
Considering this, it would be more preferable for the value of "a" to be between 0 and 1. This would reflect a decrease in the number of cars over time, potentially resulting in less traffic and smoother commuting experience.
However, it is important to note that the preference may vary depending on the specific situation and the commuting patterns on 1st Avenue. It would be beneficial to gather more detailed data and analyze the traffic trends before making a final determination.
Since the question does not specify any sources used for this answer, there is no specific APA-style reference required in this case. However, it is always good practice to cite any external sources consulted when conducting research.