y is
directly proportional to x (y varies directly as x) means
that there is a constant k (k ≠ 0), such that
(or y = kx). The constant k is called the
proportionality constant (or constant of variation).
Chem 101 with Math Reactivation
Directly and Inversely Proportional Quantities
Definition:
y is
directly proportional to x (y varies directly as x) means
that there is a constant k (k ≠ 0), such that
(or y = kx). The constant k is called the
proportionality constant (or constant of variation).
Examples:
1. The distance a bicycle travels can be stated as d = rt. If the bicycle is traveling at a rate of 15 mph then d = 15t. In one hour the bicycle travels 15 miles, in 2 hours, the bicycle travels 30 miles, and so on.
The equation, d = 15t can be written in the
form, 
. As t increases, d also increases; so the
ratio 
is constant.
2. The density of a sample of iron is 7.86
. The mass is directly proportional to its volume.
If the mass of the iron sample is doubled what happens to the volume?
Solve the following problem:
3. The volume V of a gas varies directly as the temperature T. If V=3L when T=150K.
a) Determine the proportionality constant, k.
b) Find V when T is 200K.
c) Find V when T is 100K.
(As T increases, V increases)
4. The karat rating R of a gold object varies directly as the actual percentage P of gold in the object. A 14-karat ring is 58.25% gold. What is the percentage of gold in a 24-karat gold ring?
(k = 24.03, P = 99.9%)
Definition
y is inversely
proportional to x (y varies inversely as
x) means that there is a constant k (k¹0),
such that xy = k (or 
).
Examples:
A car travels the distance of 200 miles at a constant rate
during the trip, then the traveling time can be stated as t =
. If the rate is 40 mph then t is 5 hours, if the rate
is 50 mph then t is 4 hours, and so on. The equation, t =
can be written in the form, rt = 200. Notice that as
r increases, t decreases; so the product rt is constant.
1. The volume V of a gas varies inversely with pressure P. The volume of a gas is 0.20L with a pressure of 3.0 atm. What will its volume be when the pressure is 4.2 atm?