nent used in expressing this concentration and reversing its sign. It is most often
expressed as the notation pH log 10 [H]. For example, if the hydrogen ion concen-
tration of a solution is determined to be 10^4 (or 0.0001) moles per liter, the pH is 4.Many people are familiar with the pH scale from high school, especially the prac-
tice of using special whitish paper called litmus paper to check for pH. The paper con-
tains a powder extracted from certain plants, allowing the user to determine acidity
(the paper turns red), neutrality (the paper stays white), or alkalinity (the paper turns
blue) of various solutions. The stronger the acid or base, the more intense the red or
blue, respectively. And pH isn’t just for use in chemistry class. For example, it is also
important to people who work the soil. All plants need a certain soil pH to grow and
flourish, which is why most gardeners and farmers determine the acidity or alkalinity
of their soil in order to grow better crops.What is the Universal Gas Law?
The Universal Gas Law (also called the Universal Gas Constant or the Perfect Gas
Law), is a chemical law that can also be looked at mathematically. It is represented by
the equation PV nRT, in which P is pressure, V is volume, n is the number of moles
of gas, R is the gas constant, and T is the temperature in Kelvin. (For more about the
286 Kelvin temperature scale, see “Mathematics throughout History.”)
What is radioactive decay?
M
athematics can also be applied to radioactive substances found within cer-
tain rocks. Radioactive decayis the disintegration of a radioactive sub-
stance and the emission of certain ionizing radiation (such as alpha or beta par-
ticles—or even gamma rays). Simply put, when rocks form, the minerals within
the rock often contain certain radioactive atoms that decay at a specific rate.Radioactive decay is especially important in radioactive dating, in which the
original and decayed radioactive elements are used to determine the age of the
rock. This is because certain radioactive elements will decay to a mixture of half
the original element and half another element (or isotope) in a specific time-
frame; this is also called the half-life of the original element. For example, “half”
of the Uranium-238 in a rock will decay into Lead-207 in 704 million years
(thus, the half-life of Uranium-238 is said to be 704 million years). Statistically,
this change follows a specific decay function for each isotope of an element. And
in each of these exponential functions, the time for the function’s value to
decrease to half is constant, making radioactive dating perfect in determining
the age of certain rocks.