1.3 CHAPTER 1. SKILLS FOR SCIENCE
The rate at which something happens is the number of times that it happens over a period
of time. The rate is always a change per time unit. So we can get rate of change of velocity
per unit time (∆t~v) or the rate of change in concentration per unit time (or∆tC). (Note that
∆represents a change in).
Ratios and fractions:
A fraction is a number which represents a part of a whole and is written asab, whereais
the numerator andbis the denominator. A ratio tells us the relative size of one quantity
(e.g. number of moles of reactants) compared to another quantity (e.g. number of moles of
product):2 : 1,4 : 3, etc. Ratios can also be written as fractions as percentages (fractions
with a denominator of 100).
Proportion:
Proportion is a way of describing relationships between values or between constants. We
can say thatxis directly proportional toy(x∝y) or thatais inversely proportional to
b(a ∝^1 b). It is important to understand the difference between directly and inversely
proportional.
- Directly proportional
Two values or constants are directly proportional when a change in one leads to the
same change in the other. This is a more-more relationship. We can represent this as
y∝xory=kxwherekis the proportionality constant. We have to includeksince
we do not know by how muchxchanges whenychanges.xcould change by 2 for
every change of 1 iny. If we plot two directly proportional variables on a graph, then
we get a straight line graph that goes through the origin(0; 0): - Inversely proportional
Two values or constants are inversely proportional when a change in one leads to the
opposite change in the other. We can represent this asy=kx. This is a more-less
relationship. If we plot two inversely proportional variables we get a curve that never
cuts the axis: