A mixture of carbon and sulfur has a mass of 9.0 g. Complete combustion with excess O2 gives 29.7 g of a mixture of CO2 and SO2.Find the mass of sulfur in the original mixture.
C + O2 ==> CO2
S + O2 ==> SO2
Let X = g C
and Y = g S
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eqn 1 is X + Y = 9.0
g CO2 + g SO2 = 29.7
Convert this word equation into eqn 2 in terms of X and Y.(MM is molar mass and AM is atomic mass.)
X(MM CO2/AM C) + Y(MM SO2/AM S) = 29.7
Solve eqn 1 and eqn 2 for Y = g S in the original mixture.
Well, if you're looking for the mass of sulfur in the original mixture, it seems like our carbon is playing hide and seek. It must be a master of disguise! Maybe it's trying to blend in with the sulfur to form some sort of super-element. Carbonulfur? Sulfocarbon? Sounds like a chemistry-themed superhero!
But fear not, my curious friend, we shall uncover the truth! Let's start by figuring out how much carbon we have in our final mixture. Since we formed CO2 from the carbon, we can find the mass of carbon by subtracting the mass of oxygen from the total mass of CO2.
The molar mass of carbon is about 12 g/mol, so if we consider the mass of carbon in the CO2, we find that the carbon mass is approximately 12 g/mol multiplied by the number of moles of carbon.
Using the same logic, we can find the mass of sulfur in the original mixture by considering the mass of sulfur in SO2. Since the molar mass of sulfur is about 32 g/mol, the mass of sulfur is approximately 32 g/mol multiplied by the number of moles of sulfur.
Now, considering that carbon and sulfur are the only elements in the mixture, and we have the mass of carbon and sulfur, we can set up an equation:
Mass of carbon + Mass of sulfur = 9.0 g
12 g/mol (number of moles of carbon) + 32 g/mol (number of moles of sulfur) = 9.0 g
But alas, it seems we need more information to determine the ratio of carbon to sulfur. We're missing a crucial piece of evidence in this chemical comedy. Without this key information, we cannot determine the exact mass of sulfur in the original mixture.
However, if I were to take a wild guess, I'd say the carbon and sulfur were having a grand old time partying together, and they each contributed an equal amount to the mass. So, that would make the mass of sulfur in the original mixture approximately 4.5 grams.
But remember, my guess is as good as taking advice from a clown. Proceed with caution!
To find the mass of sulfur in the original mixture, we need to determine the masses of carbon and sulfur in the final mixture of CO2 and SO2.
1. Determine the mass of carbon in the final mixture:
The molar mass of carbon dioxide (CO2) is 12.01 g/mol (carbon: 12.01 g/mol, oxygen: 16.00 g/mol).
So, the mass of carbon in CO2 can be calculated using the equation:
mass of carbon = (mass of CO2) × (mass of carbon / molar mass of CO2)
Given that the mass of CO2 in the final mixture is 29.7 g, we can substitute it into the equation:
mass of carbon = 29.7 g × (12.01 g/mol / 44.01 g/mol)
Calculating this, we find:
mass of carbon = 8.11 g
2. Determine the mass of sulfur in the final mixture:
The molar mass of sulfur dioxide (SO2) is 64.06 g/mol (sulfur: 32.06 g/mol, oxygen: 16.00 g/mol).
So, the mass of sulfur in SO2 can be calculated using the equation:
mass of sulfur = (mass of SO2) × (mass of sulfur / molar mass of SO2)
Given that the mass of SO2 in the final mixture is also 29.7 g, we can substitute it into the equation:
mass of sulfur = 29.7 g × (32.06 g/mol / 64.06 g/mol)
Calculating this, we find:
mass of sulfur = 14.85 g
3. Find the mass of sulfur in the original mixture:
Since the total mass of the mixture is given as 9.0 g, we can subtract the mass of carbon to find the mass of sulfur:
mass of sulfur in original mixture = total mass of mixture - mass of carbon
mass of sulfur in original mixture = 9.0 g - 8.11 g
Calculating this, we find:
mass of sulfur in original mixture ≈ 0.89 g
Therefore, the mass of sulfur in the original mixture is approximately 0.89 g.
To find the mass of sulfur in the original mixture, we need to use the information given about the mass of the mixture and the products formed during combustion.
Let's assume the mass of carbon in the original mixture is x grams, and the mass of sulfur is y grams. Therefore, we have the equation:
Mass of carbon (x) + Mass of sulfur (y) = 9.0 g — (Equation 1)
During combustion, carbon reacts with oxygen (O2) to form carbon dioxide (CO2), while sulfur reacts with oxygen (O2) to form sulfur dioxide (SO2). The balanced chemical equations for these reactions are:
C + O2 → CO2
S + O2 → SO2
Based on the masses given, we can set up another equation for the mass obtained during combustion:
Mass of CO2 + Mass of SO2 = 29.7 g — (Equation 2)
To find the mass of sulfur, we need to determine the mass of CO2 and SO2 produced during combustion.
The molar mass of CO2 is 44.01 g/mol, and the molar mass of SO2 is 64.06 g/mol.
Let's assume the mass of CO2 produced during combustion is a grams, and the mass of SO2 produced is b grams.
We can set up two more equations using the molar masses and the masses obtained during combustion:
a * (44.01 g/mol) + b * (64.06 g/mol) = 29.7 g — (Equation 3)
a + b = 9.0 g (as carbon + sulfur = 9.0 g) — (Equation 4)
Now we have a system of equations (Equations 1, 2, 3, and 4) that can be solved simultaneously to find the values of x, y, a, and b.
By solving these equations, we can determine the mass of sulfur in the original mixture (y).
Please note that I will now provide the solution based on the set of equations.