A. Boyle's Law PV=constant Where P= pressure and V= volume. A graph of the volume (V) ( Y-axis) of an ideal gas plotted versus its pressure (P) yields a curve that illustrates the inverse relationship between V and P. If you instead plot the 1/V (the inverse of the volume) versus P, a straight line results: V1=mP+b where m is the slope and the Y-intercept (b) should be equal to 0 . Use the following data to fill in the table. Then create a graph by plotting 1/V on the Y-axis versus P on the X-axis. Calculate the product PV for each data pair. Next calculate the average of the PV values and compare it to the reciprocal of the slope. They should be close; are they? slopeV1PV=m=mP=m1 Calculated Average of PV values = Slope (m) from graph ( to be obtained from hand-drawn graph )= Value of m1= where Nt represents the radioactivity at some time, t. No represents the initial radioactivity, and k is the radioactivity constant. If you take the ln of both sides of equation (1), we get: lnNt=lnNokt Notice that Equation 2 is a linear equation of the form y=mx+b (also called slope intercept form ). Let us express Equation 2 above as follows: lnNty=kt+lnNo=mx+b Now we can see that the y-intercept b is equal to lnNo. We can also equate m with - k, which tells us that the slope is negative. Once the value of the radioactivity decay constant k is known, the radioactivity at any other time (t) can be calculated from the Equation (1). Using the following data for a sample of Uranium-235, plot the natural log(ln) as a function of time. Table: Radioactivity Experimental Data From the graph determine the slope and y-intercept of the line of "best fit" line through the data points. slope: (Time(109years)ln(radioactivity))= y-intercept: ln( radioactivity )= What percent of the original sample remain after 1.0 billion (109) years? When you are done with this assignment, submit the following to your instructor: 1. The page on Boyl'es Law and the accompanying graph 2. The page on radioactivity decay and the the accompanying graph