percent yield for chemistry

Question

when 100 kg sand are processed with carbon and 51.4 k sic are recovered. what is the percent yield of sic

Answer 1

The percent yield of a partifular reaction equals the amount of product actually obtained, also called the actual yield, divided by the amount of product expected, also called the theoretical yield, times 100%

(Actual Yield/Theoretical Yield) * 100%

We are given the actual yield, 51.4 kg SiC, and we are given the amount of starting material, 100 kg sand), but we need to calculate the theoretical yield. Do to this, we need to a) write down the reaction, b) apply some assumptions, and c) calculate the theoretical yield.

A) Write down the reaction

This is actually somewhat tricky in this case, since there are several different reaction mechanisms which have different stoichiometric ratios between elements. However, fundamentally we can expect (when calculating theoretical yield) that all the silicon from the sand will form SiC, so the equation might look something like this:

SiO₂ + 2C --> SiC + CO₂

B) State our assumptions

Because the question did not specify how much carbon was used in the reaction, we are going to assume that carbon is NOT a limiting reagent, in other words, we assume that there is more than enough carbon for all of the sand to be converted to SiC. We are also going to assume that the sand is made of pure SiO₂, and therefore that the starting value of 1 kg of sand is all starting material for the reaction.

C) Calculate our theoretical yield

For this we need to know the molar mass of the different elements involved.

Si: 28 g/mol

O: 16 g/mol

C: 12 g/mol

We are going to use these to calculate 1) how many moles of SiO2 there are in 1 kg of sand, 2) how many moles of SiC we expect to produce, and then 3) how much that would weigh.

1)

(100. kg SiO2)*(1 mole / (28 + 16 + 16 g SiO2)) = 1670 moles SiO2

2)

There is 1 mole of Si for every 1 mole of SiO2, therefore we have 16700 moles Si

If the reaction goes to completion (and we are assuming we have plenty of carbon to make that happen), we would expect 16.7 moles of SiC at the end

3)

(16700 moles SiC) * ((28 g + 12 g)/mole(SiC)) = 66800 g SiC = 66.8 kg SiC

Finally we are ready to calculate the percent yield

Actual yield = 51.4 kg

Theoretical yield = 66.8 kg

Percent yield = (51.4 kg / 66.8 kg) * 100% = 76.9%