Solution Manual For A Mathematics Boot Camp for Science and Engineering Students, 1E by Ying Ma
Topic 1. Physical Meaning and Units
1.1. In a multi-component mixture with by either its mass fraction,
components, the concentration of component is represented
, or molar fraction,
. Let the molar mass of each component be
.
a. Find an expression to calculate
if
and
for each component in the mixture are known.
b. Find an expression to calculate
if
and
for each component in the mixture are known.
Solution a. Consider one mole of the mixture. Because the molar fraction of component is
, there are
moles of component and its mass is The mass fraction of component is then the mass of component divided by the total mass, or:
∑ b. Consider one gram of the mixture. Because the mass fraction of component is component is then
, which corresponds to
, the mass of
moles of component .
The molar fraction of component is then:
∑
Reflection This problem gives the formula to convert between mass and molar fractions. In our derivation, we assumed a fixed amount of the mixture (one mole or one gram), which simplified the reasoning. We could