A 13.8 g sample of a compound containing only N and O produced 4.2 g of nitrogen on decomposition. What is its empirical formula? What is its molecular formula if the molar mass of the compound is 92.0 g/mol
in terms of mass, N:O = 14:16 = 7:8
so, 4.2g is 7/15 of the total mass
see what you can do with that
4.2 g is N; 9.6 g is O.
g-atom N = 4.2/14 = 0.3
g-atoms O = 9.6/16 = 0.6
ratio is N1O2
So the empirical formula is NO2.
empirical mass is 14 + 16 + 16 = 46
How many of these units does it take to make a molecule if the molecule has a mass of 92. Would that be (NO2) x # units = 92 or
46 x #units = 92 and I would write (NO2)2 or N2O4.
Well, don't "compound" the problem by getting all "nit-picky"! Let's dive in and solve it with some clown chemistry!
First, we need to find the moles of nitrogen (N). We know that 4.2 g of nitrogen is produced, so we convert this to moles using the molar mass of nitrogen (N) which is 14 g/mol.
4.2 g N * (1 mol N / 14 g N) = 0.3 mol N
Next, we calculate the moles of oxygen (O) using the difference in mass between the sample and the nitrogen produced.
Sample mass - Nitrogen produced mass = Oxygen mass
13.8 g - 4.2 g = 9.6 g O
Now, let's convert this oxygen mass to moles using the molar mass of oxygen (O) which is 16 g/mol.
9.6 g O * (1 mol O / 16 g O) = 0.6 mol O
The next step is to find the ratio of the elements. Divide the number of moles by the smallest number of moles to get the simplest whole number ratios in the empirical formula.
N:O = 0.3 mol N / 0.3 mol N = 1
O:O = 0.6 mol O / 0.3 mol N = 2
Now we have an empirical formula of N1O2. However, we need to find the molecular formula based on the given molar mass of 92.0 g/mol.
To find the molecular formula, we need to determine the actual number of empirical formula units in the compound. Divide the molar mass of the compound by the empirical formula mass.
Molar mass of the compound / Empirical formula mass = Number of empirical formula units
92.0 g/mol / 30.01 g/mol (empirical formula mass of N1O2) = 3.06
Since we can't have a fraction of an empirical formula unit, we round it up to the nearest whole number. This means the molecular formula is 3(N1O2), which simplifies to N3O6.
So, the empirical formula is N1O2, and the molecular formula is N3O6. "NOS4A2" would have been a fitting molecular formula, but I guess that's already taken! 😉
To determine the empirical formula of the compound, we need to find the ratio of the elements present in it. In this case, the compound contains only nitrogen (N) and oxygen (O).
Step 1: Find the moles of nitrogen and oxygen:
The given sample of the compound weighs 13.8 g and produces 4.2 g of nitrogen upon decomposition. To find the moles of nitrogen, we divide the mass of nitrogen by its molar mass.
Molar mass of Nitrogen (N) = 14.01 g/mol
Moles of Nitrogen = Mass of Nitrogen / Molar mass of Nitrogen
= 4.2 g / 14.01 g/mol
Next, we need to find the moles of oxygen. Since the sample contains only nitrogen and oxygen, we can find the moles of oxygen by subtracting the moles of nitrogen from the moles of the compound.
Step 2: Find the moles of oxygen:
Moles of Oxygen = Moles of compound - Moles of Nitrogen
Step 3: Determine the ratio of nitrogen to oxygen:
Divide the moles of nitrogen and oxygen by the smaller value to get the simplest whole number ratio.
Step 4: Write the empirical formula:
Use the whole number ratio obtained in the previous step to write the empirical formula. The subscripts in the empirical formula represent the number of atoms of each element in the compound.
Once we have the empirical formula, we can determine the molecular formula based on the given molar mass of the compound.
Step 5: Determine the empirical formula mass:
Calculate the empirical formula mass by adding up the molar masses of the elements in the empirical formula.
Step 6: Find the ratio between the empirical formula mass and the molar mass of the compound:
Divide the molar mass of the compound by the empirical formula mass to find the ratio.
Step 7: Multiply the empirical formula by this ratio:
Multiply the subscripts in the empirical formula by the ratio found in Step 6 to obtain the molecular formula.
Let's work through the steps to determine the empirical formula and the molecular formula of the compound.
1. Moles of Nitrogen:
Moles of Nitrogen = 4.2 g / 14.01 g/mol
2. Moles of Oxygen:
Moles of Oxygen = Moles of compound - Moles of Nitrogen
3. Ratio of Nitrogen to Oxygen:
Divide the moles of nitrogen and oxygen by the smaller of the two to obtain the simplest whole number ratio.
4. Empirical Formula:
Write the empirical formula using the whole number ratio found in Step 3.
5. Empirical Formula Mass:
Calculate the empirical formula mass by adding up the molar masses of nitrogen and oxygen in the empirical formula.
6. Ratio between Empirical Formula Mass and Molar Mass:
Divide the molar mass of the compound by the empirical formula mass to find the ratio.
7. Molecular Formula:
Multiply the subscripts in the empirical formula by the ratio found in Step 6 to obtain the molecular formula.
By following these steps, you should be able to determine the empirical formula and molecular formula of the compound.