Lab 6: Sour Chemistry
The Exponential pH Change
Adapted from Real-World Math Made Easy, © 2005 Texas Instruments
START THINKING
Have you ever had an upset stomach? Common indigestion or upset stomach may be caused by too much stomach acid. Chemists measure acidity using pH on a scale from 0 to 14. A neutral substance has a pH of 7, right in the middle of the scale. A pH lower than 7 is an acidic solution, and a pH higher than 7 is a base.
When the pH level in your stomach is too low, and too acidic, you may experience upset stomach. This condition can sometimes be alleviated by taking an antacid, such as Alka-Seltzer® and water, which neutralizes the acid and raises the pH level in the stomach.
In this activity, we will use a solution of lemon juice and water to simulate an acid stomach. We will use a pH sensor to measure pH levels after an antacid tablet is added to it. The data will be modeled using a modified exponential function.
1. What will an exponential function look like on the graph?
2. If it doesn’t look like that, have you modeled an exponential function?
3. If it doesn’t look like an exponential function, what should you do?
4. What is your prediction for the relationship between time and pH?
MATERIALS
1 Nspire
1 Lab Cradle
1 pH sensor
1 cup of distilled water and lemon juice
1 antacid tablet
1 eye dropper
SET UP THE LAB
Place the Nspire into the Lab Cradle and place it on a table. Use the connectivity cable to plug in the pH sensor. Your calculator should automatically put you on the Vernier DataQuest screen, but if it doesn’t, press the c. Then press 1:New Document, NO for saving, and 7:Add Vernier DataQuest.
Your screen should look like this:
Set up the conditions for the experiment.
1. Press MENU
2. Choose 1:Experiment
3. Choose 8:Collection Setup
4. Enter 2 for Rate and 50 for Duration. Your screen should look like this.
5. TAB to OK and select it.
COLLECT THE DATA
1. Place about 125 mL of distilled water in a very clean up. The probe must be clean to get good results.
2. Loosen the top of the pH storage bottle, and carefully remove the bottle. Slide the top of the bottle up the shaft of the sensor so that the bottle top is out of the way. Do not remove the top from the sensor shaft.
3. Rinse the tip of the pH sensor with distilled water.
4. Place the pH sensor in the water, and support it so the sensor does not fall.
5. Put 20 drops of lemon juice into the water. This will simulate an acid stomach. Stir gently with the sensor.
6. Get ready to drop your antacid table into the water.
7. Push the green start button in the lower left corner of your screen. Then, drop the tablet into the water.
8. Data collection will run for 50 seconds. After collection ends, the graph will appear.
9. Use additional distilled water to rinse the pH sensor. Throw out the solution in the cup and rinse the cup. Replace the storage bottle on the pH sensor.
ANALYZE THE RESULTS
A modified exponential model can be used to model this data:
y represents the pH of the solution
x represents the time elapsed
C represents the initial pH of the solution
A represents the magnitude of the pH change
B is a value between 0 and 1 which measures the rate of change
You will need to fill out the data table to come up with a good exponential model.
y-intercept CpH approach value
A
optimized B
1. How can you figure out the y-intercept C value by using your graph?
2. How can you figure out the y-intercept C value by using your table?
3. Fill in the y-intercept value on the Data Table.
4. At the other side of the graph, the pH values should approach a constant value as the curve flattens. What do we call this line?
5. How can you use your graph to estimate this value?
6. Record this value in the Data Table.
7. As x gets larger, the model expression approaches the sum of A + C. Why is that?
8. Use the value for the approach pH and the y-intercept to determine a value for A. Enter the result in the data table.
MODEL THE DATA WITH AN EQUATION
1. Make a scatterplot of your data.
2. On the same Graphs page as your scatterplot, change the graph type to Function and enter in the generic model equation:
3. Press ENTER. Nothing new will appear on the screen.
4. Add a calculator page.
5. You will need to store the values you already determined. Enter the number you chose for C. Then press CTRL VAR which is the sto button. Then press C. Press ENTER. Then enter the number you chose for A, CTRL VAR, and A. Press ENTER. Now make a guess for the B value. Start with 0.5. Enter 0.5, CTRL VAR, B and press ENTER. Your screen will look something like this:
6. Press CTRL arrow left to go back to your graphs page. You will now see the function line. Toggle back and forth between the graphs and calculator page to adjust the value for B until you have a good fit. When you have a good one, record it on the Data Table.
QUESTIONS
1. How does the value of B affect the shape of the modeling curve?
2. How would adding more drops of lemon juice to the starting solution affect the graph? Which of the parameters A, B and C in the model expression would change? Why?
3. How would adding two antacid tablets (instead of one) to the starting solution affect the graph? Which of the parameters A, B, and C in the model expression would change? Why?
4. How would you compare the effectiveness of two different brands of antacid tablets? Which of the parameters A, B and C in the model expression would give an indication of how well a tablet works? Why?