An unknown compound contains only C, H, and O. Combustion of 4.50 g of this compound produced 10.2 g of CO2 and 4.19 g of H2O. What is this empirical formula of the unknown compound?
To find the empirical formula of an unknown compound, we need to determine the ratio of the elements present. We can start by calculating the number of moles of carbon, hydrogen, and oxygen in the given data.
1. Calculate the number of moles of CO2 produced:
- The molar mass of CO2 (carbon dioxide) is 44.01 g/mol (12.01 g/mol for carbon + 2 * 16.00 g/mol for oxygen).
- The mass of CO2 produced is 10.2 g.
- To find the moles of CO2, divide the mass by the molar mass:
Moles of CO2 = 10.2 g / 44.01 g/mol ≈ 0.232 mol.
2. Calculate the number of moles of H2O produced:
- The molar mass of H2O (water) is 18.02 g/mol (2 * 1.01 g/mol for hydrogen + 16.00 g/mol for oxygen).
- The mass of water produced is 4.19 g.
- To find the moles of H2O, divide the mass by the molar mass:
Moles of H2O = 4.19 g / 18.02 g/mol ≈ 0.232 mol.
3. Calculate the moles of carbon in the compound:
- Since each CO2 molecule contains one carbon atom, the moles of carbon is the same as the moles of CO2.
Moles of carbon = 0.232 mol.
4. Calculate the moles of hydrogen in the compound:
- Each H2O molecule contains two hydrogen atoms.
- Therefore, the moles of hydrogen in the compound are twice the moles of H2O:
Moles of hydrogen = 2 * 0.232 mol = 0.464 mol.
5. Calculate the moles of oxygen in the compound:
- To find the moles of oxygen, we subtract the moles of carbon and hydrogen from the total moles:
Moles of oxygen = 0.464 mol - 0.232 mol = 0.232 mol.
Now that we have the moles of each element, we can determine the empirical formula.
6. Divide the moles of each element by the smallest mole value:
- In this case, the smallest mole value is 0.232 mol (the moles of carbon and oxygen).
- Divide the moles of carbon, hydrogen, and oxygen by 0.232 mol to get the mole ratios:
Carbon: 0.232 mol / 0.232 mol = 1
Hydrogen: 0.464 mol / 0.232 mol = 2
Oxygen: 0.232 mol / 0.232 mol = 1
The empirical formula of the unknown compound is CH2O.
To determine the empirical formula of the unknown compound, we need to find the ratio of the number of atoms of each element present in the compound.
1. Start by determining the number of moles of CO2 and H2O produced:
- Moles of CO2 = mass of CO2 / molar mass of CO2
- Moles of H2O = mass of H2O / molar mass of H2O
2. Calculate the number of moles of carbon (C) and hydrogen (H) based on the moles of CO2 and H2O produced:
- Moles of C = 1 mole of C per 1 mole of CO2
- Moles of H = 2 moles of H per 1 mole of H2O
3. Calculate the mass of oxygen (O) by subtracting the total mass of C and H from the total mass of the compound:
- Mass of O = Total mass of the compound - Mass of C - Mass of H
4. Convert the moles of C, H, and O into their simplest whole number ratio by dividing each value by the smallest number of moles obtained.
5. Use the resulting whole number ratio to determine the empirical formula of the unknown compound.
Let's go through the calculations step by step.
Given:
Mass of CO2: 10.2 g
Molar mass of CO2: 44.01 g/mol
Mass of H2O: 4.19 g
Molar mass of H2O: 18.02 g/mol
1. Calculate the number of moles of CO2 and H2O:
- Moles of CO2 = 10.2 g / 44.01 g/mol = 0.2319 mol
- Moles of H2O = 4.19 g / 18.02 g/mol = 0.232 mol
2. Calculate the number of moles of C and H:
- Moles of C = 0.2319 mol of CO2 × 1 mol of C/1 mol of CO2 = 0.2319 mol
- Moles of H = 0.232 mol of H2O × 2 mol of H/1 mol of H2O = 0.464 mol
3. Calculate the mass of O:
- Mass of O = Total mass of the compound - Mass of C - Mass of H
- Total mass of the compound = mass of CO2 + mass of H2O = 10.2 g + 4.19 g = 14.39 g
- Mass of O = 14.39 g - (0.2319 g * 12.01 g/mol) - (0.464 g * 1.01 g/mol) = 3.333 g
4. Convert the moles of C, H, and O into their simplest whole number ratio:
- Divide each value by the smallest number of moles, which is 0.2319 mol:
- Moles of C = 0.2319 mol / 0.2319 mol = 1
- Moles of H = 0.464 mol / 0.2319 mol = 2
- Moles of O = 3.333 g / 0.2319 mol = 14.375
5. Determine the empirical formula of the unknown compound:
- The whole number ratio is C1H2O14, which can be simplified to CHO7.
Therefore, the empirical formula of the unknown compound is CHO7.
First, determine grams C, H, and O.
g CO2 = 10.2 x (atomic mass C/molar mass CO2) = about 2.8 but you need to be more accurate than that. The other numbers will be estimates, also; therefore you need to go through the problem and get the right numbers.
g H = 4.19 x (2*atomic mass H/molar mass H2O) = about 0.47
g O = 4.50 - g H - g C = about 1.3.
Next, convert g C, H, O to mols.
mols C = about 2.7/12 = about 0.23
mols H = about .47/1 = about 0.47
mols O = about 1.3/16 = about 0.08
Now find the ratio of the elements to each other with the smallest number being 1.00. The easy way to do that is to divide the smallest number by itself (which makes it 1.0000 every time), then divide the other two numbers by the same small number. Round to whole numbers and that will be the empirical formula.
Post your work if you get stuck and I can help you through it.