When 1.578 grams of a hydrocarbon, CxHy, were burned in a combustion analysis apparatus, 4.951 grams of CO2 and 2.027 grams of H2O were produced. In a separate experiment, the molar mass of the compound was found to be 56.11 g/mol. Determine the empirical formula and the molecular formula of the hydrocarbon.
(4.951 / molar mass CO2) = moles C = x
(2.027 / molar mass H2O) / 2 = moles H = y
k[x(molar mass C) + y(molar mass H)] = 56.11
molecular formula is ... C(kx)H(ky)
divide kx and ky by GCF to find empirical formula
To determine the empirical formula and molecular formula of the hydrocarbon, we can follow these steps:
Step 1: Find the moles of CO2 produced.
Molar mass of CO2 (carbon dioxide) = 12.01 g/mol + 2 * 16.00 g/mol = 44.01 g/mol
Moles of CO2 = Mass of CO2 / Molar mass of CO2 = 4.951 g / 44.01 g/mol
Step 2: Find the moles of H2O produced.
Molar mass of H2O (water) = 2 * 1.01 g/mol + 16.00 g/mol = 18.02 g/mol
Moles of H2O = Mass of H2O / Molar mass of H2O = 2.027 g / 18.02 g/mol
Step 3: Convert moles of CO2 and H2O to moles of carbon and hydrogen respectively.
From the balanced chemical equation of combustion, we know that:
1 mole of CO2 contains 1 mole of carbon (C)
1 mole of H2O contains 2 moles of hydrogen (H)
Moles of carbon (C) = Moles of CO2
Moles of hydrogen (H) = 2 * Moles of H2O
Step 4: Determine the ratio of carbon to hydrogen.
Divide the moles of carbon and hydrogen by the smaller of the two values to get a whole number ratio.
Step 5: Determine the empirical formula.
Write the empirical formula using the ratio obtained in step 4 as subscripts.
Step 6: Calculate the empirical formula mass.
The empirical formula mass is the sum of the atomic masses of all the atoms in the empirical formula. Use the periodic table to determine the atomic masses.
Step 7: Determine the number of empirical formula units in one mole of the compound.
The number of empirical formula units is equal to the molar mass of the compound divided by the empirical formula mass.
Step 8: Determine the molecular formula.
Multiply the subscripts in the empirical formula by the number of empirical formula units calculated in step 7.
Let's calculate it.
Step 1: Moles of CO2 = 4.951 g / 44.01 g/mol = 0.1124 mol
Step 2: Moles of H2O = 2.027 g / 18.02 g/mol = 0.1124 mol
Step 3: Moles of carbon (C) = 0.1124 mol
Moles of hydrogen (H) = 2 * 0.1124 mol = 0.2248 mol
Step 4: Dividing both by 0.1124, we get 1: 2 (C:H) ratio.
Step 5: Empirical formula = CH2
Step 6: Empirical formula mass = 12.01 g/mol + 2 * 1.01 g/mol = 14.03 g/mol
Step 7: Number of empirical formula units in one mole = 56.11 g/mol / 14.03 g/mol = 4
Step 8: Molecular formula = (CH2) * 4 = C4H8
Therefore, the empirical formula of the hydrocarbon is CH2 and the molecular formula is C4H8.
To determine the empirical and molecular formulas of the hydrocarbon CxHy, we need to follow a series of steps:
Step 1: Calculate the number of moles of CO2 and H2O produced.
Given:
Mass of CO2 = 4.951 grams
Mass of H2O = 2.027 grams
Using the molar mass of CO2 and H2O, we can calculate the number of moles for each compound:
Molar mass of CO2 = 44.01 g/mol
Molar mass of H2O = 18.02 g/mol
Number of moles of CO2 = Mass of CO2 / Molar mass of CO2
Number of moles of CO2 = 4.951 g / 44.01 g/mol
Number of moles of H2O = Mass of H2O / Molar mass of H2O
Number of moles of H2O = 2.027 g / 18.02 g/mol
Step 2: Calculate the empirical formula of the hydrocarbon.
The empirical formula represents the simplest whole-number ratio of the elements in a compound. To determine it, we need to find the ratio of carbon to hydrogen.
From the balanced chemical equation of the combustion reaction, we know that:
1 mole of CxHy will produce x moles of CO2
1 mole of CxHy will produce y/2 moles of H2O
Now, we can set up a ratio using the number of moles of CO2 and H2O:
Number of moles of CxHy / Number of moles of CO2 = x
Number of moles of CxHy / Number of moles of H2O = y/2
Solving these equations, we find:
Number of moles of CxHy = (Number of moles of CO2) x (1/x) (since x moles of CO2 is produced from 1 mole of CxHy)
Number of moles of CxHy = (Number of moles of H2O) x (2/y) (since y/2 moles of H2O is produced from 1 mole of CxHy)
Step 3: Find the empirical formula mass.
The empirical formula mass is the sum of the atomic masses of all the atoms in the empirical formula.
The empirical formula mass can be calculated as follows:
Empirical formula mass = (Number of moles of CxHy) x (Molar mass of compound)
Step 4: Determine the empirical formula.
The empirical formula is found by dividing the empirical formula mass by the molar mass of the compound.
Step 5: Determine the molecular formula.
The molecular formula represents the actual number of atoms of each element in a compound.
To calculate the molecular formula, we need to know the molar mass of the compound, which is given as 56.11 g/mol. Divide the molar mass of the compound by the empirical formula mass to find the number of empirical formula units in one molecule.
Molecular formula = Empirical formula x (Molar mass of compound / Empirical formula mass)
By following these steps and performing the calculations, you can determine both the empirical and molecular formulas of the hydrocarbon CxHy.