Ibuprofen, the active ingredient in Advil, is made up of carbon, hydrogen, and oxygen atoms. When a sample of ibuprofen, weighing 5.000 g, burns in oxygen, 13.86g of CO2 and 3.926 g of water are obtained. What is the simplest formula of ibuprofen?
I need to find out if I'm doing everything right here:
13.86g CO2 + 3.926g H2O
percent of C in CO2 is 12 / (12 + 2*16) = 30%
# of grams C = 13.86 * 30% = 4.16 g
moles C = 4.16 / 12 = 0.347
percent of H in H2O is 2/ (1(2) + 16) = 11.11%
# of grams H = 3.926 * 11.11% = 0.436 g
moles H = .436/1 = 0.436
# of grams O = 5.000 – (grams H + grams C) = 5.000 – 4.596 = 0.404 g
moles O = .404/16 = .0253
C = .347 / .0253 = 13.7
H = .436 / .0253 = 17.2
O = .0253 / .0253 = 1
C14H17O
I got this formula, but I looked up ibuprofen and saw that it has a C13H18O2 formula, so did I miss a doubling of oxygen moles somewhere, or maybe I'm just flat out wrong? please help!!
Two things. I don't get 30% for C in CO2 but more likle 27.27%. That will change mass C AND it will change mass O when you subtract to obtain grams O. Your H calculations look ok and the rest of the problem is ok. When I did it I obtained C13H18O2 and I looked it up on the web and found that is the formula. I don't know where you found the C14 number.
http://en.wikipedia.org/wiki/Ibuprofen
I hope this helps.
yes that solved everything thanks!
Your calculations are mostly correct, but you made a small mistake in determining the number of grams of oxygen (O). Let's go through the calculations step by step:
Given:
Mass of ibuprofen (C13H18O2) = 5.000 g
Mass of CO2 produced = 13.86 g
Mass of H2O produced = 3.926 g
Step 1: Calculate the moles of carbon (C)
Mass of carbon in CO2 = 12 g/mol * (13.86 g CO2 / 44.01 g/mol) = 3.77 g
Moles of carbon = 3.77 g / 12 g/mol = 0.314 mol
Step 2: Calculate the moles of hydrogen (H)
Mass of hydrogen in H2O = 2 g/mol * (3.926 g H2O / 18.015 g/mol) = 0.437 g
Moles of hydrogen = 0.437 g / 1 g/mol = 0.437 mol
Step 3: Calculate the moles of oxygen (O)
Mass of oxygen = 5.000 g - (mass of carbon + mass of hydrogen)
= 5.000 g - (3.77 g + 0.437 g) = 0.793 g
Moles of oxygen = 0.793 g / 16 g/mol = 0.050 mol
Step 4: Divide the moles of each element by the smallest number of moles
Dividing the moles of each element by 0.050 mol:
Carbon (C): 0.314 mol / 0.050 mol = 6.28 (approximately)
Hydrogen (H): 0.437 mol / 0.050 mol = 8.74 (approximately)
Oxygen (O): 0.050 mol / 0.050 mol = 1
Step 5: Round the numbers to the nearest whole number to get the empirical formula
The empirical formula is C6H9O.
The empirical formula C6H9O is a simplified ratio of the elements in the compound. To find the molecular formula, you need the molar mass of the compound. Given that ibuprofen has a molar mass of 206.28 g/mol, you can divide this by the empirical formula mass (C6H9O = 6 * 12.01 + 9 * 1.01 + 16.00 = 111.15 g/mol).
Molecular formula = (molar mass of ibuprofen) / (molar mass of empirical formula)
Molecular formula = 206.28 g/mol / 111.15 g/mol = 1.86 (approximately)
So the simplest formula of ibuprofen is C6H9O, and its molecular formula is C13H18O2.
Let's go through the calculations step by step to find the simplest formula of ibuprofen.
First, you correctly determined the grams of carbon (C) in the carbon dioxide (CO2) produced:
Grams of C = 13.86 g CO2 * (12 g C / 44.01 g CO2) = 3.76 g C
Next, you calculated the moles of carbon:
Moles of C = 3.76 g C / 12.01 g/mol = 0.313 mol C
Moving on to hydrogen (H), you calculated the grams of H in the water (H2O) produced:
Grams of H = 3.926 g H2O * (2 g H / 18.02 g H2O) = 0.436 g H
And the moles of hydrogen:
Moles of H = 0.436 g H / 1.01 g/mol = 0.432 mol H
Finally, you found the grams of oxygen (O) by subtracting the grams of H and C from the original sample:
Grams of O = 5.000 g - (0.436 g H + 3.76 g C) = 0.804 g O
And the moles of oxygen:
Moles of O = 0.804 g O / 16.00 g/mol = 0.050 mol O
Now, let's check the ratios of moles of C, H, and O to find the simplest formula.
The ratio of moles of C to moles of O is approximately 0.313 mol C / 0.050 mol O = 6.26
The ratio of moles of H to moles of O is approximately 0.432 mol H / 0.050 mol O = 8.64
These ratios are not in whole numbers, which means we need to multiply them by the same factor to get whole number ratios. In this case, multiplying by 2 gives us:
Approximate whole number ratio of C to O = 6.26 * 2 = 12.52, rounded to 13
Approximate whole number ratio of H to O = 8.64 * 2 = 17.28, rounded to 17
So, the simplest formula based on these ratios would be C13H17O. This matches the formula you initially obtained.
However, as you mentioned, the correct empirical formula for ibuprofen is C13H18O2. It seems that your calculation for the moles of hydrogen (H) might have been inaccurate.
Double-check the calculation for moles of H:
Moles of H = 0.436 g H / 1.008 g/mol = 0.432 mol H
With this corrected value for moles of H, let's recalculate the ratios:
Ratio of moles of C to moles of O = 0.313 mol C / 0.050 mol O = 6.26, rounded to 6
Ratio of moles of H to moles of O = 0.432 mol H / 0.050 mol O = 8.64, rounded to 9
Now, multiplying both ratios by 2 to obtain whole number ratios:
Whole number ratio of C to O = 6 * 2 = 12
Whole number ratio of H to O = 9 * 2 = 18
Therefore, the simplest formula of ibuprofen is C12H18O.