Silicon carbide (SiC) is made by reacting sand (Silicon dioxide, SiO2) with powdered carbon at high temperature. Carbon monoxide is also formed. What is the percent yield if 51.4kg of SiC is recovered from processing 100.0kg of sand? What mass (in kg) of carbon would be needed for this process?
I tried creating the equation and got this:
SiO2+3C->SiC+2CO
......SiO2 + 3C->SiC + 2CO
a. mols SiC = 100,000 g/molar mass SiO2 = ?
Look at the equation 1 mol SiO2 produces 1 mol SiC; therefore, ? mols SiO2 will produce that many mols SiC.
Convert mols SiC to grams. grams SiC = mols SiC x molar mass SiC = ?. This is the theoretical yield(TY). The actual yield (AY) is 51,400 g from the problem.
% yield = (AY/TY)*100
b.
Convert mols SiO2 you calculated from above to mols C using the coefficients in the balanced equation the same way you converted mols SiO2 to mols SiC above. Then convert mols C to grams C the same way you converted mols SiC to grams SiC above. Post your work if you get stuck.
Well, it seems like your equation is on point. Now onto the calculations!
To determine the percent yield, we need to compare the actual yield (51.4kg) with the theoretical yield. The theoretical yield is the maximum amount of product that could be obtained based on the reaction stoichiometry.
Looking at the balanced equation, we can see that 1 mole of SiO2 reacts with 3 moles of C to produce 1 mole of SiC. Using the molar masses, we can convert the 100.0kg of SiO2 to moles:
100.0kg SiO2 x (1 mole SiO2 / 60.08 kg SiO2) = 1665.78 moles SiO2
According to the stoichiometry, every mole of SiO2 requires 3 moles of C. Therefore, the theoretical moles of C required for this reaction would be:
1665.78 moles SiO2 x (3 moles C / 1 mole SiO2) = 4997.34 moles C
Now we can convert the theoretical moles of C to mass:
4997.34 moles C x (12.01 g C / 1 mole C) = 59975.22 g C
To convert grams to kilograms, we divide by 1000:
59975.22 g C / 1000 = 59.98 kg C
So, approximately 59.98 kg of carbon would be needed for this process.
Now, let's calculate the percent yield:
Percent Yield = (Actual Yield / Theoretical Yield) x 100
Percent Yield = (51.4kg / 59.98kg) x 100 = 85.68%
Hooray! You've got an approximate percent yield of 85.68%. However, just remember that this calculation assumes ideal conditions, and in reality, the yield might be influenced by various factors.
To calculate the percent yield, we can use the formula:
Percent Yield = (Actual Yield / Theoretical Yield) x 100
First, we need to determine the theoretical yield of SiC. According to the balanced equation:
1 mole of SiO2 reacts with 3 moles of C to produce 1 mole of SiC.
To find the number of moles of SiO2 in 100.0kg, we need to divide the mass of SiO2 by its molar mass. The molar mass of SiO2 is 60.08 g/mol.
Mass of SiO2 = 100.0kg x 1000 g/kg = 100,000 g
Number of moles of SiO2 = 100,000 g / 60.08 g/mol = 1664.11 mol
According to the balanced equation, the ratio of SiO2 to SiC is 1:1. Therefore, the theoretical yield of SiC is also 1664.11 mol.
To convert moles of SiC to grams, we multiply by the molar mass of SiC, which is 40.10 g/mol.
Theoretical Yield of SiC = 1664.11 mol x 40.10 g/mol = 66,677.51 g
Now we need to convert grams to kilograms for easier comparison:
Theoretical Yield of SiC = 66,677.51 g / 1000 = 66.68 kg
To calculate the percent yield:
Percent Yield = (Actual Yield / Theoretical Yield) x 100
Percent Yield = (51.4 kg / 66.68 kg) x 100 = 77.02%
Therefore, the percent yield is 77.02%.
To find the mass of carbon needed for this process, we need to use the stoichiometry of the balanced equation.
The molar mass of carbon (C) is 12.01 g/mol.
According to the balanced equation, the ratio of C to SiC is 3:1. Therefore, for every 3 moles of C, we can produce 1 mole of SiC.
To find the number of moles of C needed, we use the molar ratio:
3 moles of C = 1 mole of SiC
x moles of C = 1664.11 mol of SiC
x = 1664.11 mol of SiC x (3 mol of C / 1 mol of SiC) = 4992.33 mol of C
To convert moles of C to grams, we multiply by the molar mass of C:
Mass of C = 4992.33 mol x 12.01 g/mol = 59,923.27 g
Now we need to convert grams to kilograms for the final answer:
Mass of C = 59,923.27 g / 1000 = 59.92 kg
Therefore, approximately 59.92 kg of carbon would be needed for this process.
To find the percent yield, we need to compare the amount of SiC actually obtained with the theoretical yield, which is the maximum amount of SiC that can be obtained from the given amount of sand.
First, let's calculate the theoretical yield of SiC:
1 mole of SiO2 reacts with 3 moles of C to produce 1 mole of SiC.
From the balanced chemical equation, we can see that the molar ratio of SiO2 to SiC is 1:1. So, the number of moles of SiC that can be formed is equal to the number of moles of SiO2.
To find the number of moles of SiO2, we need to convert the mass of sand (SiO2) to moles using the molar mass of SiO2.
Molar mass of SiO2 = Atomic mass of Si + (2 x Atomic mass of O) = 28.09 g/mol + (2 x 16.00 g/mol) = 60.09 g/mol
Number of moles of SiO2 = Mass of SiO2 / Molar mass of SiO2 = 100.0 kg / 60.09 g/mol = 1666 mol
Since the molar ratio of SiO2 to SiC is 1:1, the number of moles of SiC formed will also be 1666 mol.
Now, let's calculate the mass of SiC that corresponds to 1666 moles:
Mass of SiC = Number of moles of SiC x Molar mass of SiC
The molar mass of SiC is the sum of the atomic masses of silicon and carbon:
Molar mass of SiC = Atomic mass of Si + Atomic mass of C = 28.09 g/mol + 12.01 g/mol = 40.10 g/mol
Mass of SiC = 1666 mol x 40.10 g/mol ≈ 66,697.6 g or 66.7 kg
Therefore, the theoretical yield of SiC is approximately 66.7 kg.
To find the percent yield, we can use the formula:
Percent yield = (Actual yield / Theoretical yield) x 100%
Given that the actual yield of SiC is 51.4 kg and the theoretical yield is 66.7 kg:
Percent yield = (51.4 kg / 66.7 kg) x 100% ≈ 77.0%
So, the percent yield of SiC in this process is approximately 77.0%.
To calculate the mass of carbon required, we can use the stoichiometric ratio from the balanced equation.
From the balanced equation, we can see that 1 mole of SiC is formed from 3 moles of C.
The number of moles of C required can be calculated using the molar mass of C:
Molar mass of C = 12.01 g/mol
Number of moles of C = (3 moles of C / 1 mole of SiC) x (1666 mol of SiC)
Number of moles of C = 3 x 1666 mol ≈ 4998 mol
Now, let's calculate the mass of carbon required:
Mass of C = Number of moles of C x Molar mass of C
Mass of C = 4998 mol x 12.01 g/mol ≈ 59,976 g or 59.98 kg
Therefore, approximately 59.98 kg of carbon would be needed for this process.