# 2.76 g of K_2CO_3 was treated by a series of reagents so as to convert all of its carbon to K_2Zn_3[Fe(CN)_6]_2. Calculate the weight of the product?

Jul 18, 2015

The mass of the product is 1.16 g.

#### Explanation:

All you really have to do to solve this problem is figure out how much carbon you had in the 2.76-g sample of potassium carbonate.

Once you do that, you use the fact that all of the carbon present in the potassium carbonate sample is now a part of the final product.

So, use carbon and potassium carbonate's molar masses to determine the percent composition of carbon in the compound

(12.011cancel("g/mol"))/(138.206cancel("g/mol")) * 100 = "8.69% C"

Potassium carbonate contains 8.69 g of carbon for every 100 g of compound. This means that your sample contained

2.76cancel("g"K_2CO_3) * "8.69 g C"/(100cancel("g"K_2CO_3)) = "0.2398 g C"

All this carbon is now found in the final product. Once again, use molar masses to determine the carbon percent composition of ${K}_{2} Z {n}_{3} {\left[F e {\left(C N\right)}_{6}\right]}_{2}$.

Keep in mind, however, that you have a total of 12 carbon atoms in the final product!

(12 * 12.011cancel("g/mol"))/(698.235cancel("g/mol")) * 100 = "20.64% C"

Once again, this tells you that you have 20.64 g of carbon for every 100 g of product.

Therefore,

$0.2398 \cancel{\text{g C") * "100 g product"/(20.64cancel("g C")) = color(green)("1.16 g product}}$