Water At 25°C Has A PH Of 7—anything That Has

Water At 25 Degrees Celsius Has A Ph Of 7 Anything That Has A Ph Lowe

Water at 25 degrees Celsius has a pH of 7. Anything that has a pH lower than 7 is called acidic, while pH's above 7 are basic or alkaline. Seawater has a pH just over 8, while lemonade has a pH of approximately 3. Create a graph of the pH function. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph. A pool company forgets to bring their logarithmic charts, but they need to raise the amount of hydronium ions in a pool by 0.50. Using complete sentences, explain how your graph can be used to solve 10 – y = 0.50. Find the approximate solution. The pool company has developed new chemicals that transform the pH scale. Using the pH function p(t) = –log 10 t as the parent function, explain which transformation would result in a y-intercept. Use complete sentences and show all translations on your graph.

Paper For Above instruction

The relationship between pH and hydrogen ion concentration ([H+]) in solutions can be described by the logarithmic function p(t) = –log₁₀ t, where t represents the concentration of hydronium ions. This mathematical relationship forms the basis for understanding and visualizing the pH scale, which ranges typically from 0 to 14 in most natural solutions, with 0 indicating highly acidic conditions and 14 indicating strong alkalinity. To facilitate understanding, constructing a graph of the pH function over an appropriate domain is essential to visually interpret the behavior of hydrogen ion concentrations across different solutions.

Graphing the pH Function:

The graph of p(t) = –log₁₀ t is a decreasing curve that asymptotically approaches negative infinity as t approaches zero and increases slowly as t grows larger. In order to visualize where the pH values are 0 and 1 on this graph, the first step involves identifying the corresponding hydrogen ion concentrations. When pH = 0, it implies that the concentration of [H+] is 1 mol/L because pH = –log₁₀ [H+], so if pH = 0, then [H+] = 10^0 = 1 mol/L. Similarly, when pH = 1, the hydrogen ion concentration equals 10^–1 = 0.1 mol/L. On the graph, these points can be located at t = 1 for pH 0 and t = 0.1 for pH 1.

Zooming In on the Graph:

Given the typical range of hydrogen ion concentrations in solutions ranging from 10^–14 to 1 mol/L, zooming into the section between t = 0.01 and t = 1 is practical for detailed analysis. For instance, to accurately locate pH values around 0 and 1, focusing on this logarithmic region helps visualize how small changes in hydrogen ion concentration translate into pH differences.

Application to Pool Chemistry:

Suppose a pool's pH needs to be increased slightly, effectively raising the concentration of hydronium ions by 0.50 in the pH scale. Because pH is logarithmic, an increase in pH by 0.50 corresponds to reducing the hydrogen ion concentration by a factor of approximately 10^–0.50 ≈ 0.316. To find the new concentration after an increase of 0.50 in pH, the original ion concentration is divided by this factor.

Using the Graph to Solve 10 – y = 0.50:

In this scenario, if y represents the pH value that needs to be calculated, then 10 – y = 0.50 can be rearranged to y = 10 – 0.50 = 9.50. Although this may seem out of the usual pH range, it exemplifies how the graph of p(t) can help in interpreting how much the concentration of [H+] must change, as pH values correspond to specific points on the logarithmic graph. To approximate the solution, locate the point where pH = 9.50 on the graph, which corresponds to the hydrogen ion concentration t = 10^–9.50 ≈ 3.16 × 10^–10 mol/L.

Transformations of the pH Function:

The parent function p(t) = –log₁₀ t can be modified to produce different environmental effects in the scale. The transformations include:

- p(t) + 1: This vertical translation shifts the entire graph upward by 1 unit, effectively increasing the pH values by 1, which would mimic a solution becoming more alkaline.

- p(t + 1): This horizontal translation shifts the graph left by 1 unit, changing the concentration t to t + 1, hence affecting how pH responds to specific hydrogen concentrations.

- –1: This is a simple vertical shift downward by 1 unit when added directly to the function, decreasing every pH value equivalently.

- p(t): This is the unaltered parent function, representing the standard logarithmic relationship in pH measurements.

Conclusion:

Understanding the graph of p(t) = –log₁₀ t allows for visualizing and solving real-world problems related to acidity and alkalinity, particularly in contexts like pool maintenance and chemical adjustments. By interpreting shifts and transformations of the function, water chemistry can be controlled more precisely through graphical comprehension of hydrogen ion concentrations. These graphical tools provide valuable insights into the logarithmic behavior of pH, making complex chemical interactions more accessible and manageable.

References

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  • National Institute of Standards and Technology (NIST). (2023). pH scale definitions and applications. Retrieved from https://www.nist.gov
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