| If
either the rate
constant or the
half-life is known, the other can be calculated. Half-lives usually
are used because they have an immediate physical meaning. The exponential decay curve (fig 4 opposite) can be used to give the rate law a physical meaning. The rate of change of concentration with time, d[C-14]/dt, is simply the slope of the first-order decay curve at any time, t. Because carbon-14 is disappearing, the
slope is negative. By drawing a tangent line to the decay curve
at several points and examining the slope, you should be able to
verify that the slope of the curve at any time t is proportional
to the remaining concentration of carbon-14, measured in the vertical
direction. This is what the rate law for a first-order process means:
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