A hydrocarbon is burnt completely in air to form 13.2g of carbon dioxide gas and 7.2g of water. What is the molecular formula of the hydrocarbon?
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Since it is a hydrocarbon that burns and combines with oxygen in the air, so all the carbon in carbon dioxide derives from the hydrocarbon, and similarly for hydrogen in water.
Now for CO2,
proportion of carbon/CO2
=12/(12+2*16)
=12/44
=3/11
Mass of carbon in hydrocarbon
=mass of CO2 * 3/11
= 13.2 * 3/11
= 3.6 g
Similarly,
proportion of H2 in H2O
= 2*1/(2*1+16)
= 2/18
= 1/9
Mass of H2 in hydrocarbon
= 7.2 * 1/9
= 0.8 g
Ratio of number of carbon atoms to number of hydrogen atoms
= (3.6/12) / (0.8/1)
= 0.3 /0.8
= 3/8
So the empirical formula is
C3H8 or any multiple there of.
To determine the molecular formula of the hydrocarbon, we need to follow a step-by-step approach.
Step 1: Calculate the number of moles of carbon dioxide gas (CO2):
- The molar mass of carbon dioxide (CO2) is:
- Atomic mass of carbon (C) = 12 g/mol
- Atomic mass of oxygen (O) = 16 g/mol
- Molar mass of CO2 = (12 g/mol × 1) + (16 g/mol × 2) = 44 g/mol
- The number of moles of CO2 can be calculated using the formula:
- Moles of CO2 = Mass of CO2 (g) / Molar mass of CO2 (g/mol)
- Moles of CO2 = 13.2 g / 44 g/mol = 0.3 mol
Step 2: Calculate the number of moles of water (H2O):
- The molar mass of water (H2O) is:
- Atomic mass of hydrogen (H) = 1 g/mol
- Atomic mass of oxygen (O) = 16 g/mol
- Molar mass of H2O = (1 g/mol × 2) + (16 g/mol × 1) = 18 g/mol
- The number of moles of H2O can be calculated using the formula:
- Moles of H2O = Mass of H2O (g) / Molar mass of H2O (g/mol)
- Moles of H2O = 7.2 g / 18 g/mol = 0.4 mol
Step 3: Determine the empirical formula of the hydrocarbon:
- The empirical formula represents the simplest whole number ratio of atoms in a compound.
- To find the empirical formula, we need to determine the ratios of carbon to hydrogen in the hydrocarbon.
- To calculate the ratios, we can divide the number of moles of carbon dioxide (CO2) and water (H2O) by their respective coefficients.
- Moles of Carbon (C) = 0.3 mol
- Moles of Hydrogen (H) = 0.8 mol (2 moles of H for each mole of H2O)
- The ratio of Carbon to Hydrogen can be simplified to:
- Carbon (C): Hydrogen (H) = 0.3/0.3 : 0.8/0.3 ≈ 1 : 2.67
- Multiplying the ratio by 3, we get:
- Carbon (C): Hydrogen (H) ≈ 3 : 8
Step 4: Determine the empirical formula of the hydrocarbon:
- The empirical formula shows the whole number ratio of atoms in a molecule.
- Based on the carbon and hydrogen ratio obtained in the previous step (C : H ≈ 3 : 8), the empirical formula of the hydrocarbon is C3H8.
Therefore, the molecular formula of the hydrocarbon is C3H8, which corresponds to propane.
To find the molecular formula of the hydrocarbon, we need to determine the number of carbon and hydrogen atoms present in the molecule.
First, let's start by calculating the number of moles of carbon dioxide gas (CO2) and water (H2O) produced.
1. Calculate the number of moles of carbon dioxide gas (CO2):
The molar mass of carbon dioxide (CO2) is:
1 atom of carbon (C) = 12.01 g/mol
2 atoms of oxygen (O) = 2 × 16.00 g/mol
Total molar mass of CO2 = 12.01 g/mol + (2 × 16.00 g/mol) = 44.01 g/mol
The number of moles of CO2 = mass of CO2 / molar mass of CO2
Number of moles of CO2 = 13.2 g / 44.01 g/mol
2. Calculate the number of moles of water (H2O):
The molar mass of water (H2O) is:
2 atoms of hydrogen (H) = 2 × 1.01 g/mol
1 atom of oxygen (O) = 16.00 g/mol
Total molar mass of H2O = (2 × 1.01 g/mol) + 16.00 g/mol = 18.02 g/mol
The number of moles of H2O = mass of H2O / molar mass of H2O
Number of moles of H2O = 7.2 g / 18.02 g/mol
Now, let's determine the ratio of carbon and hydrogen atoms in the hydrocarbon.
3. Find the mole ratio of carbon to hydrogen:
The chemical formula of a hydrocarbon is CxHy, where x represents the number of carbon atoms and y represents the number of hydrogen atoms.
From the balanced equation of the combustion reaction of a hydrocarbon, we know that for each mole of CO2 produced, x moles of carbon are present in the hydrocarbon.
Similarly, for each mole of H2O produced, (2y) moles of hydrogen are present in the hydrocarbon (since there are two hydrogen atoms in one molecule of water).
Therefore, the mole ratio of carbon to hydrogen is:
(Number of moles of CO2 produced) / x = (Number of moles of H2O produced) / (2y)
4. Solve for x and y:
Substitute the calculated values from steps 1 and 2 into the mole ratio equation.
[(13.2 g / 44.01 g/mol) / x] = [(7.2 g / 18.02 g/mol) / (2y)]
Simplify the equation to solve for x and y.
5. Find the whole number ratios:
Once you find the values of x and y, divide them by their greatest common divisor to get the simplest whole number ratio.
For example, if x = 2 and y = 4, the simplest ratio would be x:y = 1:2.
This simplest whole number ratio will represent the molecular formula of the hydrocarbon.