Lesson 7-3

Boyle's Law

     You Probably started experimenting with Boyle's Law when you were a small child.  When you squeeze a balloon, you might notice that the harder you push, the harder it seems to push back.  When you lie back on an inflatable mattress, or pool float, it compresses up to a point and then seems to stop.  This is because as you decrease the volume of a confined gas, the pressure that it exerts increases.   This relationship, called Boyle's Law, is summarized by the statement:The volume of a sample of gas is inversely proportional to its pressure, if temperature remains constant. 
     When two variables are inversely proportional, like pressure and volume in the example above, the product of the two variables will always remain constant.   Because of the relationship between the pressure and volume of a gas sample at constant temperature, if you double the value of one, you divide the other by two.   The chart below will demonstrate the inverse relationship between the volume and pressure of a gas.  Imagine a gas sample trapped in a cylinder which allows you to adjust the pressure.  Notice how the pressure changes cause the volume to change, while the product of the two variables will remain a constant (K).

     Boyle's law is sometimes used to determine the volume that a gas would have at another pressure.  If you were to collect a sample of gas under the atmospheric conditions in your lab on a given day, you might want to mathematically determine what the volume of the gas would be under different conditions.  The formula that can be used to calculate the affects of pressure changes on the volume of a gas at constant temperature is shown below:

P₁V₁ = P₂V₂
Were P = Pressure and V =Volume

     Example 1 - A sample of gas collected in a 350 cm³ container exerts a pressure of 103 kPa.  What would be the volume of this gas at 150 kPa of pressure?  (Assume that the temperature remains constant.)

Solving:

Write the original formula:                                            P₁V₁ = P₂V₂

Then list what is given and what is unknown.

P₁ = 103 kPa

V₁= 350 cm³

P₂ = 150 kPa

V₂ = ?

Next, predict what should happen.  The pressure is going up by nearly 1/3, so the volume should go down by a bit less than 1/3.

Now, Adjust the original formula to isolate the unknown, solve and round to the correct number of significant digits.

a)  P₁V₁ = P₂V₂

b)  P₁V₁ = P₂V_{2
        -------         --------}
               P₂               P₂         

c) V₂ = P₁V₁
               -------
             P₂

P₁ = 103 kPa                                                         V₂ = 103 kPa x 350 cm³
                                                                                       -------------------------
V₁= 350 cm³                                                                           150 kPa

P₂ = 150 kPa                                                        V₂ = 240.333333 cm³

V₂ = ?                                                                    V₂ = 240 cm³

Finally, check to see that the results match your prediction.  The volume did go down by close to 1/3.

     Of course, the original formula can be solved for a different unknown.  For example, you can determine what the pressure would have to be in order to end up with a certain volume.

    Example 2 - A sample of neon has a volume of 239 cm³ at 2.00 atm of pressure.  What would the pressure have to be in order for the gas to have a volume of 5.00 x 10² cm³?

Solving:

Write the original formula:                                            P₁V₁ = P₂V₂

Then list what is given and what is unknown.

P₁ =  2.00 atm

V₁= 239 cm³

P₂ = ?

V₂ = 5.00 x 10² cm³

Next, predict what should happen.    You want the volume to more than double, so the pressure would have to be less than half the original.

Now, Adjust the original formula to isolate the unknown, solve and round to the correct number of significant digits.

a)  P₁V₁ = P₂V₂

b) P₁V₁ = P₂V₂
        --------   --------
       V₂         V₂

c) P₂ =  P₁V_{1
                     ----------}
                    V₂

P₁ =  2.00 atm                                                                    P₂ = 2.00 atm x 239 cm³
                                                                                                   ------------------------
V₁= 239 cm³                                                                                5.00 x 10² cm³

P₂ = ?                                                                                 P₂ = 0.956 atm

V₂ = 5.00 x 10² cm³                                                          P₂ = 0.956 atm

Finally, check to see that the results match your prediction.  The pressure would have to be less than 1/2.

Now try some examples from the links below.

Please forward all questions, comments and criticisms to Gregory L. Curran.
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Last Modified February 07, 2008