You take an aspirin tablet (a compound consisting solely of carbon, hydrogen, and oxygen) with a mass of 1.00 g, combust it under an oxygen atmosphere, and collect 2.20 g of carbon dioxide and 0.400 g water. The molar mass of aspirin is between 170 and 190 g/mol. The molecular formula of aspirin is
g C = 2.20g CO2 x (atomic mass C/molar mass CO2) = about 0.6g
g H = 0.4g H2O x (2 atomic mass H/molar mass H2O) = 0.044
g O = 1.00g - g C - g H
Note: you need to redo all of this more accurately than I've done them.
Convert to mols
mols C = 0.6/12 = about 0.05
mols H = 0.044/1 = about 0.044
mols O = 0.356/16 = about 0.0222
Now find the ratio. The easy way is to divide by the smallest number.
0.044/0.0222 = 2 = H
0.05/0.0222 = 2.25 = C
0.0222/0.0222 = 1.0 = O
You can't round these to whole numbers BUT you can muliply by 1, 2, 3, 4, etc until you get whole numbers.
Try it and you will find multiply by4 gives H = 2*4 = 8
C = 2.25*4 = 9
O = 1*4 = 4
C9H8O4 should be the empirical formula.
Empirical formula mass is
(9*12) + (8*1) + (4*16) = 180
That falls withing the 170-190 range given in the problem therefore, there is only one grouping of C9H8O4 per molecule. The empirical formula is the same as the molecular formula.
Good!
You take an aspirin tablet (a compound consisting solely of carbon, hydrogen, and oxygen) with a mass of 1.00 g, burn it in air, and collect 2.20 g of carbon dioxide and 0.400 g water. The molar mass of aspirin is between 170 and 190 g/mol. The molecular formula of aspirin is
Well, well, well! It seems we have a case of aspirin combustion on our hands! Let's crack this case together, shall we?
So, we start off with a 1.00 g aspirin tablet (CₙHₘOₚ) and burn it up in the presence of oxygen. After the smoke clears, we're left with 2.20 g of carbon dioxide (CO₂) and 0.400 g of water (H₂O).
Now, let me dust off my detective hat and get to work!
First things first, we need to determine the number of moles of carbon dioxide and water produced. To do that, we need to know the molar mass of aspirin, which is somewhere between 170 and 190 g/mol.
Now, if the molar mass of aspirin was an actual suspect, it'd be sitting in the molar line-up looking nervous! But alas, we don't know the exact value, so we'll have to estimate.
Let's assume the molar mass of aspirin is around 180 g/mol, just to keep things spicy.
We can calculate the number of moles of CO₂ produced by dividing its mass (2.20 g) by its molar mass (44 g/mol), which gives us 0.050 moles. Similarly, the number of moles of water produced is 0.400 g divided by its molar mass of 18 g/mol, giving us 0.022 moles.
Now, now, don't be impatient! We'll get to the molecular formula soon enough. We just need to figure out the molar ratios here. For every mole of aspirin, we get one mole of CO₂ and one mole of water. So, the number of moles of aspirin must be the same as the number of moles of the products.
Since we found 0.050 moles of CO₂ and 0.022 moles of H₂O, that means we have 0.022 moles of aspirin.
Now, let's do some more math magic! We need to find the empirical formula of aspirin. To do that, we divide the number of atoms in each element by their greatest common divisor.
For carbon, we have 0.050 moles (since the ratio is 1:1) and for oxygen, we have 0.022 moles (again, a 1:1 ratio). This gives us a ratio of 1:1:1.
So, the empirical formula of aspirin is C₁H₁O₁. But wait, there's more!
The empirical formula only gives us the smallest whole-number ratio of atoms, not the actual number of atoms in the molecule. Since we know the molecular mass of aspirin is between 170 and 190 g/mol, we can calculate the molecular formula possibilities.
By dividing these molecular masses by the empirical formula mass of 29 g/mol, we get a range of 6-7 for carbon, hydrogen, and oxygen. Therefore, the most likely molecular formula of aspirin is C₇H₆O₃.
Case closed! It looks like we've cracked this molecular mystery, thanks to some math, chemistry, and a touch of clownery. Keep those brain cells firing, and remember, science can be a hilarious detective game too!
To determine the molecular formula of aspirin, we need to analyze the information provided and calculate the empirical formula first. The empirical formula represents the simplest whole number ratio of atoms in a compound.
Given:
Mass of carbon dioxide (CO2) collected = 2.20 g
Mass of water (H2O) collected = 0.400 g
Mass of aspirin (C9H8O4) = 1.00 g
Now, let's find the moles of carbon dioxide and water:
For carbon dioxide (CO2):
Molar mass of CO2 = 12.01 g/mol (carbon) + 2 * 16.00 g/mol (oxygen) = 44.01 g/mol
Moles of CO2 = Mass of CO2 / Molar mass of CO2
Moles of CO2 = 2.20 g / 44.01 g/mol ≈ 0.050 moles
For water (H2O):
Molar mass of H2O = 2 * 1.01 g/mol (hydrogen) + 16.00 g/mol (oxygen) = 18.02 g/mol
Moles of H2O = Mass of H2O / Molar mass of H2O
Moles of H2O = 0.400 g / 18.02 g/mol ≈ 0.022 moles
Now, let's find the moles of carbon, hydrogen, and oxygen present in the aspirin:
Moles of carbon in aspirin = Moles of CO2 (produced) = 0.050 moles
Moles of hydrogen in aspirin = Moles of H2O (produced) = 0.022 moles
To find the moles of oxygen in aspirin, we need to subtract the moles of carbon and hydrogen from the total moles of the compound (assumed to be 1 mole):
Moles of oxygen in aspirin = 1 mole - (moles of carbon + moles of hydrogen)
Moles of oxygen in aspirin = 1 mol - (0.050 mol + 0.022 mol) ≈ 0.928 moles
Now, let's calculate the empirical formula of aspirin by dividing the moles of each element by the smallest number of moles (0.022 moles) to get the simplest whole number ratio:
Carbon: 0.050 moles / 0.022 moles ≈ 2.273 ≈ 2
Hydrogen: 0.022 moles / 0.022 moles = 1
Oxygen: 0.928 moles / 0.022 moles ≈ 42.182 ≈ 42
Therefore, the empirical formula of aspirin is C2H1O42.
To determine the molecular formula, we need to know the molar mass of the compound. The given range is 170 to 190 g/mol. By calculating the molar mass of the empirical formula, we can determine how many empirical units are needed to reach this range.
Molar mass of empirical formula = (2 * 12.01 g/mol) + (1 * 1.01 g/mol) + (42 * 16.00 g/mol) = 180.44 g/mol
To find the molecular formula, divide the molar mass of the aspirin by the molar mass of the empirical formula:
Molecular formula ratio = Molar mass of aspirin / Molar mass of empirical formula
Molecular formula ratio = (170 to 190 g/mol) / 180.44 g/mol
By performing this calculation, we can determine the number of empirical formula units needed to match the molar mass range given for aspirin.