Lab: Mass of a Text Book

Using a Gas to Find the Mass of a Text Book

Objective
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.

Materials

1. 2-3 drops glycerine	5. clamp/holder
2. a laboratory syringe	6. 4 or more text books
3. septum to cover exit of syringe	7. lab notebook
4. ring stand	8. 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.

What is the pressure in the syringe before any books are placed on the plunger? (Atmospheric pressure is usually slightly below 760 mmHg).
Will the pressure in the syringe increase or decrease as each book is added?
How will we be able to measure the pressure inside the syringe?
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; V_cyl = πr²h).
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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Procedure

Use a few drops of glycerine the lubricate the plunger of the syringe
Seal the tip of the syringe with the septum
Set up the ring stand with the holder and clamp and put the syringe vertically in the clamp
Seal the tip of the syringe with the septum
Record the volume of air in the syringe without pressing down on the plunger at all
Balance one textbook on the plunger of the syringe and gently press down on it, letting the plunger spring back up
Record the volume of gas and the number of books and leave space for another value and an average in your data table
Sequentially add more books in the same way and record the volume of gas and the number of books
Once you have added the last book, remove them again one by one
Record the volume next to the number of books as you remove each one; record the average of this value and the initial value you recorded; this will be the volume used in your calculations

Analysis
According to Boyle’s Law, the volume of a gas is inversely proportional to its pressure. This can be written as an equation:

1
—  = kP
V

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 P_a 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 P_a + B, for two books it is P_a + 2B, and so on. This can be written in a general form as P_a + nB, where n is the number of books. This expression can be substituted into the law given above:

 1                           1
———  = k(P_a + nB)     →     ———  = kBn + kP_a      
 V_n                          V_n

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 kP_a. Since you know P_a, 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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