Video Transcript
Calcium metal can be used to
produce pure rubidium from its chloride according to the equation: Ca solid plus two
RbCl solid reacting to give CaCl2 solid plus two Rb liquid. What is the atom economy for the
production of rubidium by this process, to the nearest percentage unit?
This question asks us to determine
the atom economy for the production of rubidium. Atom economy is a measure of the
amount of starting materials or reactants which are converted to useful or desirable
products. The expression or equation for atom
economy can be expressed in several different ways. One way is to say atom economy is
equal to the total relative formula mass of the desired or useful product or
products divided by the total relative formula mass of all the reactants. And we can multiply by 100 percent
to get the answer in terms of a percentage.
So first we need to determine the
total relative formula mass of the desired product. And in this example, the desired
product is Rb or rubidium. When we calculate the value for the
numerator, we will need to take into account the coefficient of two in front of
rubidium. We will also need to calculate the
total relative formula mass of all the reactants. And the reactants are Ca or calcium
and RbCl, which is rubidium chloride. Again, we will need to take into
consideration the stoichiometric coefficient of two in front of rubidium
chloride.
Let’s clear some space to do the
calculations for the relative formula masses of the substances in the numerator and
in the denominator. So let’s start by calculating the
relative formula mass of the desired product rubidium. Taking into account the coefficient
of two, we can put in the relative formula mass — in this case, just the relative
atomic mass — of rubidium, which is 85.468. And we get this from the periodic
table. We get a value of 170.936, and this
is unitless.
Let’s now do the same calculation
for both of the reactants, calcium and rubidium chloride. Calcium has a mass value of 40.078
from the periodic table. And for rubidium chloride, we will
multiply the values by two because of the coefficient two. Rubidium’s mass value is 85.468,
and chlorine, 35.45 from the periodic table. When we solve, we get 241.836. Now we can use the atom economy
expression and plug in our values into the numerator and denominator.
The total relative formula mass of
the desired product rubidium is 170.936. So we put this in the
numerator. And the total relative formula mass
of all the reactants will be the sum of the relative formula mass of each reactant,
calcium and rubidium chloride, whose mass values we have calculated. Adding the two denominator values,
we get a total value of 281.914. Taking the numerator divided by the
denominator, we get an answer of 60.6 percent, which is the atom economy for the
production of rubidium by this process.
However, the question asks us to
express the answer to the nearest percentage unit. So rounding up, we get an answer of
61 percent. What does this answer mean? The answer tells us that 61 percent
of the starting materials ended up as the useful desired target product,
rubidium. Finally, the atom economy for the
production of rubidium by the process given in the equation is 61 percent.
