1. Silicon dioxide reacts with carbon upon heating to produce silicon carbide (SiC) and carbon monoxide.
SiO2(s) + 3C(s) = SiC(s) + 2CO(g)
a. What mass of carbon is required to react completely with 15.70 g of SiO2?
b. When 152 g of SiO2 reacts with excess carbon, what mass of SiC is produced?
c. If 42.2 g of CO were produced by this reaction, what mass of carbon must have reacted?
how many moles of SiO2?
Each mole needs 3 moles of C.
similarly for the other parts. work with moles, then back to grams.
a) 14.6 g
B) 23.76 g
C) 38.54 g
To determine the mass of carbon required or produced, we will use the stoichiometry of the balanced chemical equation:
SiO2(s) + 3C(s) → SiC(s) + 2CO(g)
a. To find the mass of carbon required to react completely with 15.70 g of SiO2:
Step 1: Convert the mass of SiO2 to moles using the molar mass of SiO2.
Molar mass of SiO2 = (28.09 g/mol) + (2 × 16.00 g/mol) = 60.09 g/mol
Moles of SiO2 = Mass / Molar mass = 15.70 g / 60.09 g/mol = 0.2614 mol
Step 2: Use the stoichiometric ratio from the balanced chemical equation to determine the moles of carbon.
From the equation, the stoichiometric ratio of SiO2 to C is 1:3.
Moles of C = 3 × Moles of SiO2 = 3 × 0.2614 mol = 0.7842 mol
Step 3: Convert the moles of carbon to mass using the molar mass of carbon.
Molar mass of C = 12.01 g/mol
Mass of C = Moles of C × Molar mass of C = 0.7842 mol × 12.01 g/mol = 9.415 g
Therefore, 9.415 grams of carbon is required to react completely with 15.70 grams of SiO2.
b. To find the mass of SiC produced when 152 g of SiO2 reacts with excess carbon:
Step 1: Convert the mass of SiO2 to moles using the molar mass of SiO2.
Moles of SiO2 = Mass / Molar mass = 152 g / 60.09 g/mol = 2.532 mol
Step 2: Use the stoichiometric ratio from the balanced chemical equation to determine the moles of SiC.
From the equation, the stoichiometric ratio of SiO2 to SiC is 1:1.
Moles of SiC = Moles of SiO2 = 2.532 mol
Step 3: Convert the moles of SiC to mass using the molar mass of SiC.
Molar mass of SiC = (28.09 g/mol) + (12.01 g/mol) = 40.10 g/mol
Mass of SiC = Moles of SiC × Molar mass of SiC = 2.532 mol × 40.10 g/mol = 101.43 g
Therefore, 101.43 grams of SiC is produced when 152 grams of SiO2 reacts with excess carbon.
c. To find the mass of carbon that reacted when 42.2 g of CO is produced:
Step 1: Convert the mass of CO to moles using the molar mass of CO.
Molar mass of CO = 28.01 g/mol
Moles of CO = Mass / Molar mass = 42.2 g / 28.01 g/mol = 1.507 mol
Step 2: Use the stoichiometric ratio from the balanced chemical equation to determine the moles of carbon.
From the equation, the stoichiometric ratio of CO to C is 2:3.
Moles of C = (3/2) × Moles of CO = (3/2) × 1.507 mol = 2.2605 mol
Step 3: Convert the moles of carbon to mass using the molar mass of carbon.
Molar mass of C = 12.01 g/mol
Mass of C = Moles of C × Molar mass of C = 2.2605 mol × 12.01 g/mol = 27.14 g
Therefore, 27.14 grams of carbon must have reacted to produce 42.2 grams of CO.
a. To determine the mass of carbon required to react completely with 15.70 g of SiO2, we need to use the balanced chemical equation:
SiO2(s) + 3C(s) = SiC(s) + 2CO(g)
From the equation, we can see that the mole ratio between SiO2 and C is 1:3. This means that for every mole of SiO2, we need 3 moles of C.
Step 1: Convert the mass of SiO2 to moles using the molar mass of SiO2.
Molar mass of SiO2 = 28.0855 g/mol (from periodic table)
Number of moles of SiO2 = Mass of SiO2 / Molar mass of SiO2
Number of moles of SiO2 = 15.70 g / 28.0855 g/mol
Step 2: Use the mole ratio from the balanced equation to calculate the moles of C required.
Number of moles of C = Number of moles of SiO2 x (3 moles of C / 1 mole of SiO2)
Step 3: Convert the moles of C to mass using the molar mass of carbon.
Molar mass of C = 12.01 g/mol (from periodic table)
Mass of carbon = Number of moles of C x Molar mass of C
b. To determine the mass of SiC produced when 152 g of SiO2 reacts with excess carbon, we need to follow these steps:
Step 1: Convert the mass of SiO2 to moles using the molar mass of SiO2.
Number of moles of SiO2 = Mass of SiO2 / Molar mass of SiO2
Step 2: Use the mole ratio from the balanced equation to calculate the moles of SiC produced.
From the balanced equation, we can see that the mole ratio between SiO2 and SiC is 1:1. This means that 1 mole of SiO2 produces 1 mole of SiC.
Step 3: Convert the moles of SiC to mass using the molar mass of SiC.
Molar mass of SiC = atomic mass of Si + atomic mass of C
Molar mass of SiC = 28.0855 g/mol + 12.01 g/mol
Mass of SiC = Number of moles of SiC x Molar mass of SiC
c. To determine the mass of carbon that must have reacted, given that 42.2 g of CO were produced, we can use the following steps:
Step 1: Convert the mass of CO to moles using the molar mass of CO.
Molar mass of CO = 28.01 g/mol (from periodic table)
Number of moles of CO = Mass of CO / Molar mass of CO
Step 2: Use the mole ratio from the balanced equation to calculate the moles of C that reacted.
From the balanced equation, we can see that the mole ratio between CO and C is 2:3. This means that for every 2 moles of CO produced, 3 moles of C must have reacted.
Step 3: Convert the moles of C to mass using the molar mass of carbon.
Molar mass of C = 12.01 g/mol (from periodic table)
Mass of carbon = Number of moles of C x Molar mass of C