Question #44455

The process is as simple as it sounds - you just take each volume value and take its reciprocal to be your new x-coordinate. An example will probably help show what to do:

Imagine you have a sealed container with a piston attached, so that you can change the volume and read out the pressure. We start with one liter of gas at atmospheric pressure. If we work in liters for volume and atmospheres for pressure we have a starting point of:

#(1L, 1atm.)#

for our #(x,y)# coordinates. We can then change the volume and get the pressure values:

When we graph this we get:

This is the expected behaviour for Boyle's law which states:

#P*V= k#

where #k# is a constant. We can rearrange this as:

#P=k/V#

The trick we are looking for is to "linearize" this equaition by taking our new #x# values as #x'=1/V# such that:

#P = k*x'#

This is the equation of a straight line through the origin, which makes it very easy to experimentally determine #k# for instance. To to this we take each #V# value and calculate it's reciprocal an put it in a table:

Then when we plot #P# vs. #1//V# we get:

For more information you can look here