Using a Gas to Find the Mass of a Text Book

Books will be placed on the plunger of the syringe one by one and the volume of the gas will be recorded. This will illustrate Boyle's Law which governs the relationship between the pressure and volume of a gas. The data will be used to determine the mass of a text book.

1. 2-3 drops glycerine5. clamp/holder
2. a laboratory syringe6. 4 or more text books
3. septum to cover exit of syringe7. lab notebook
4. ring stand8. safety gear

Pre-Lab Questions
Write your answers to these questions neatly on a separate piece of paper, showing all steps of all calculations. Be sure to do the calculations before the experiment and to re-write them if they aren’t neat and easy to read.
  1. What is the pressure in the syringe before any books are placed on the plunger? (Atmospheric pressure is usually slightly below 760 mmHg).
  2. Will the pressure in the syringe increase or decrease as each book is added?
  3. How will we be able to measure the pressure inside the syringe?
  4. What is the area of the top of the plunger? (Hint: You know the volume of the syringe in cm3 and you can find the height between 0 mL and 30 mL; Vcyl = πr2h).
  5. The density of mercury (Hg) is 13.6 g/cm3. Say you have measured a pressure equal to a column of mercury that is 350 mm tall. Find the mass of the column of mercury if it has the same cross-sectional area as the plunger of your syringe.

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According to Boyle’s Law, the volume of a gas is inversely proportional to its pressure. This can be written as an equation:
—  = kP
where k is a proportionality constant. This law can be used to find the mass of a textbook. The starting pressure will be taken to be 755 mmHg (call it Pa for atmospheric pressure). For each book you add, you add a certain amount of pressure to the syringe. Call this amount B. So for one book the pressure in the syringe is Pa + B, for two books it is Pa + 2B, and so on. This can be written in a general form as Pa + nB, where n is the number of books. This expression can be substituted into the law given above:
 1                           1
———  = k(Pa + nB)     →     ———  = kBn + kPa      
 Vn                          Vn           
The second way of writing this equation has the form of a straight line (y = mx + b). Plot the data you collected on a graph with 1/V on the x-axis and the number of books on the y-axis. You will have to calculate 1/V first. The slope of the line is equal to kB and the y-intercept is kPa. Since you know Pa, you can find k (in units of 1/mL). The constant k will have units of mL/mmHg. B will have units of mmHg/book. The slope will be in units of mL/book.

To find the mass of a book, find the value of B using the information above. This will be in units of pressure (mmHg) and you need units of mass. Use the model given in pre-lab question five to find the mass of the equivalent column of mercury. This mass is the same as the mass of the book. Check the result by finding the mass of the book using a balance. Discussion
Write a lab report on a separate piece of paper and be sure to create and include a neat, readable data table. For this lab you will also need the graph you made in class. Keep this lab for future reference. The lab report should include the usual sections. (See previous labs).
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