A 99.99% pure, 0.4903 g sample containing only carbon, hydrogen, and nitrogen is subjected to combustion analysis, resulting in the formation of 1.373 g CO2, 0.2791 g H2O, and 0.1860 g NO. What is the empirical formula of the sample?
Here is what I would do.
The weight of the sample is 0.4903 x 0.9999 = 0.49025.
mols C = 1.373/44.01 = ?
mols H = 0.2791 x 2.016/18.02 = ?
mols N = 0.1860/14.007 = ?
Now find the ratio of each with no number being less than 1.00. The easy way to do that is to divide the smallest number by itself. Then divide the other numbers by the same small number. Round to whole numbers to find the empirical formula. I came up with C5H5N
but I wouldn't be satisfied with that (that's pyridine). Why? Because g carbon + g nitrogen + g H don't add to 0.4903 but to a larger number. I would redo the elemental analysis. If I calculate these grams I get 0.3747 g C, 0.03122 g H and 0.0868 g N and that adds to 0.4927g. In my book that's too far from 0.4903 g. I wouldn't sleep right at night.
To find the empirical formula, we need to determine the number of moles of each element present in the sample.
1. Calculate the number of moles of CO2:
- The molar mass of CO2 is 44.01 g/mol.
- Divide the mass of CO2 (1.373 g) by the molar mass of CO2 to find the number of moles of CO2: 1.373 g / 44.01 g/mol = 0.03119 mol CO2.
2. Calculate the number of moles of H2O:
- The molar mass of H2O is 18.02 g/mol.
- Divide the mass of H2O (0.2791 g) by the molar mass of H2O to find the number of moles of H2O: 0.2791 g / 18.02 g/mol = 0.01549 mol H2O.
3. Calculate the number of moles of NO:
- The molar mass of NO is 30.01 g/mol.
- Divide the mass of NO (0.1860 g) by the molar mass of NO to find the number of moles of NO: 0.1860 g / 30.01 g/mol = 0.006199 mol NO.
4. Calculate the number of moles of carbon (C):
- Each mole of CO2 contains 1 mole of carbon.
- The number of moles of C is equal to the number of moles of CO2: 0.03119 mol C.
5. Calculate the number of moles of hydrogen (H):
- Each mole of H2O contains 2 moles of hydrogen.
- The number of moles of H is equal to 2 times the number of moles of H2O: 2 * 0.01549 mol H = 0.03098 mol H.
6. Calculate the number of moles of nitrogen (N):
- Each mole of NO contains 1 mole of nitrogen.
- The number of moles of N is equal to the number of moles of NO: 0.006199 mol N.
7. Divide the number of moles of each element by the smallest number of moles obtained:
- Smallest number of moles = 0.006199 mol (N).
- Divide moles of each element by 0.006199 mol:
C: 0.03119 mol / 0.006199 mol = 5
H: 0.03098 mol / 0.006199 mol = 5
N: 0.006199 mol / 0.006199 mol = 1
Therefore, the empirical formula of the sample is C5H5N.
To determine the empirical formula of the sample, we need to calculate the moles of each element present in the compound.
1. Start by calculating the moles of carbon dioxide (CO2):
- The molar mass of CO2 is 44.01 g/mol (12.01 g/mol for carbon and 2 * 16.00 g/mol for oxygen).
- Divide the mass of CO2 by its molar mass to get moles of CO2:
moles of CO2 = mass of CO2 / molar mass of CO2 = 1.373 g / 44.01 g/mol = 0.0312 mol CO2
2. Next, calculate the moles of water (H2O):
- The molar mass of H2O is 18.02 g/mol (2 * 1.01 g/mol for hydrogen and 16.00 g/mol for oxygen).
- Divide the mass of H2O by its molar mass to get moles of H2O:
moles of H2O = mass of H2O / molar mass of H2O = 0.2791 g / 18.02 g/mol = 0.0155 mol H2O
3. Lastly, determine the moles of nitrogen monoxide (NO):
- The molar mass of NO is 30.01 g/mol (14.01 g/mol for nitrogen and 16.00 g/mol for oxygen).
- Divide the mass of NO by its molar mass to get moles of NO:
moles of NO = mass of NO / molar mass of NO = 0.1860 g / 30.01 g/mol = 0.0062 mol NO
4. Calculate the moles of each element:
- The mole ratio of carbon in CO2 is 1:1, so the moles of carbon in the sample is equal to the moles of CO2 (0.0312 mol CO2).
- The mole ratio of hydrogen in H2O is 2:1, so the moles of hydrogen in the sample is twice the moles of H2O (2 * 0.0155 mol H2O = 0.0310 mol H).
- The mole ratio of nitrogen in NO is 1:1, so the moles of nitrogen in the sample is equal to the moles of NO (0.0062 mol NO).
5. Find the ratio of moles:
- Divide the number of moles for each element by the smallest number of moles. In this case, the smallest number of moles is 0.0062 mol.
- Ratio of carbon = 0.0312 mol / 0.0062 mol = 5
- Ratio of hydrogen = 0.0310 mol / 0.0062 mol = 5
- Ratio of nitrogen = 0.0062 mol / 0.0062 mol = 1
6. Write the empirical formula:
Based on the ratios found, the empirical formula of the compound is C5H5N.