Question

[20pts] I want to start counterfeiting American pennies. Each penny weighs 2.56g and I want $200.00 of pennies for my scheme. Set up a dimensional analysis solution to figure out how many grams of aluminum I'll need to make this amount of pennies.
$2Al(s) + 3CuCl_{2}(aq)$ ⇒ $2AlCl_{3}(aq) + 3Cu(s)$

I need help setting up the equation using dimensional analysis. Any help is appreciated!

Answer 1

Answer:

    $\ 200.00\times 100\dfrac{penny}{\ }\times \dfrac{2.56g}{penny}\times \dfrac{1molCu}{63.5gCu}\times \dfrac{2molAl}{3molCu}\times \dfrac{27gAl}{1molAl}$

Explanation:

The dimensional analysis helps you by focusing your attention into the units: you must set up the equation starting with the available units and add the factors with the units such that the cancelation of numerators and denominators ends up with the desired units: grams of aluminium in this case.

In this case, you start with a mass of 2.56 grams per penny, which is $2.56g/penny$, whose value is $200.00 and want to end with the grams of

Aluminium needed.

Then, you must use the mole ratios derived from the chemical equation in a way that the units lead from grams of copper to grams of aluminium.

The equation is:

           $2Al(s)+3CuCl_2(aq)\rightarrow 2AlCl_3(aq)+3Cu(s)$

From which, the mole ratio between copper and aluminium is:

           $2molAl(s):3molCu(s)\\\\\dfrac{2molAl}{3molCu},or\\\\\\\dfrac{3molCu}{2molAl}$

You must also use the atomic masses of Cu and Al which are 63.5g/mol and 27g/mol respectively.

The equation is:

     

          $\ 200.00\times 100\dfrac{penny}{\ }\times \dfrac{2.56g}{penny}\times \dfrac{1molCu}{63.5gCu}\times \dfrac{2molAl}{3molCu}\times \dfrac{27gAl}{1molAl}$

You can check that afeter multiplying all the factors, the most units will cancel and the final units will be grams of Al.