A sample of an unknown compound, composed only of carbon and hydrogen, produced 26.8 g of CO₂ and 16.5 g of
H₂O in a combustion analysis. What is the empirical formula of the unknown compound?
To find the empirical formula of the unknown compound, we need to determine the ratio of carbon to hydrogen in the compound.
First, we need to find the number of moles of CO2 and H2O produced in the combustion analysis.
1 mol of CO2 is composed of 1 mol of carbon and 2 mol of oxygen.
The molar mass of oxygen is 16 g/mol, so the mass of 2 mol of oxygen is 2 * 16 g/mol = 32 g/mol.
Therefore, 1 mol of CO2 is composed of 1 mol of carbon and 32 g/mol of oxygen.
The molar mass of CO2 is 12 g/mol (carbon) + 32 g/mol (oxygen) = 44 g/mol.
Using the given mass of CO2 (26.8 g), we can calculate the number of moles of CO2:
26.8 g CO2 * (1 mol CO2/44 g CO2) = 0.6091 mol CO2.
1 mol of H2O is composed of 2 mol of hydrogen and 1 mol of oxygen.
The molar mass of hydrogen is 1 g/mol, so the mass of 2 mol of hydrogen is 2 * 1 g/mol = 2 g/mol.
Therefore, 1 mol of H2O is composed of 2 g/mol of hydrogen and 16 g/mol of oxygen.
The molar mass of H2O is 2 g/mol (hydrogen) + 16 g/mol (oxygen) = 18 g/mol.
Using the given mass of H2O (16.5 g), we can calculate the number of moles of H2O:
16.5 g H2O * (1 mol H2O/18 g H2O) = 0.9167 mol H2O.
Now, we need to determine the ratio of carbon to hydrogen in the compound. Since the empirical formula represents the simplest ratio of elements, we can divide the number of moles of each element by the smallest number of moles.
Dividing the number of moles of carbon by 0.6091 mol (the smallest number of moles):
0.6091 mol CO2 / 0.6091 mol = 1 mol carbon.
Dividing the number of moles of hydrogen by 0.6091 mol (the smallest number of moles):
0.9167 mol H2O / 0.6091 mol = 1.503 mol hydrogen.
The ratio of carbon to hydrogen in the unknown compound is approximately 1:1.503.
Since we need to express the empirical formula in whole numbers, we can multiply both the carbon and hydrogen ratio by 2 to get the simplest whole number ratio:
2 mol carbon : 3 mol hydrogen.
Therefore, the empirical formula of the unknown compound is C2H3.
To determine the empirical formula of the unknown compound, we need to find the mole ratios between carbon and hydrogen in the CO₂ and H₂O produced.
Step 1: Convert the mass of CO₂ and H₂O to moles:
- Moles of CO₂ = Mass of CO₂ / molar mass of CO₂
- Moles of H₂O = Mass of H₂O / molar mass of H₂O
The molar mass of CO₂ is 44 g/mol, and the molar mass of H₂O is 18 g/mol.
Moles of CO₂ = 26.8 g CO₂ / 44 g/mol CO₂
Moles of H₂O = 16.5 g H₂O / 18 g/mol H₂O
Step 2: Determine the number of moles of carbon and hydrogen in the CO₂ and H₂O.
- Carbon atoms in CO₂: 1
- Hydrogen atoms in H₂O: 2
Moles of carbon = Moles of CO₂
Moles of hydrogen = 2 * Moles of H₂O
Step 3: Calculate the mole ratio between carbon and hydrogen using the lowest number of moles.
- Divide the moles of carbon and hydrogen by their lowest value to obtain a whole number ratio.
Moles of carbon = Moles of CO₂ / Moles of CO₂
Moles of hydrogen = (2 * Moles of H₂O) / Moles of CO₂
Step 4: Find the empirical formula using the mole ratio obtained in Step 3.
- Multiply the ratio values by whole numbers, if necessary, to obtain the simplest whole number ratio.
For example, if the moles ratio calculated is CₓHᵧ, multiply it by 2 if both values are not whole numbers.
The empirical formula of the unknown compound will be CₓHᵧ.