A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g...
Given information:
- Upon combustion, a gaseous hydrocarbon produces 0.72 g of water and 3.08 g of carbon dioxide.
- We need to determine the empirical formula of the hydrocarbon.
Steps to solve the problem:
1. Calculate the number of moles of water and carbon dioxide produced.
2. Determine the ratio of moles of carbon and hydrogen in the hydrocarbon.
3. Find the empirical formula based on the mole ratios.
Solution:
Step 1: Calculate the number of moles of water and carbon dioxide produced.
- The molar mass of water (H2O) is 18 g/mol (2 g/mol for hydrogen and 16 g/mol for oxygen).
- The molar mass of carbon dioxide (CO2) is 44 g/mol (12 g/mol for carbon and 32 g/mol for oxygen).
Moles of water = mass of water / molar mass of water
= 0.72 g / 18 g/mol
= 0.04 mol
Moles of carbon dioxide = mass of carbon dioxide / molar mass of carbon dioxide
= 3.08 g / 44 g/mol
= 0.07 mol
Step 2: Determine the ratio of moles of carbon and hydrogen in the hydrocarbon.
- In water, the ratio of hydrogen to oxygen is 2:1, so the number of moles of hydrogen is twice the number of moles of water.
Moles of hydrogen = 2 * moles of water
= 2 * 0.04 mol
= 0.08 mol
- In carbon dioxide, the ratio of carbon to oxygen is 1:2, so the number of moles of carbon is the same as the number of moles of carbon dioxide.
Moles of carbon = moles of carbon dioxide
= 0.07 mol
Step 3: Find the empirical formula based on the mole ratios.
- The empirical formula represents the simplest whole number ratio of atoms in a compound.
- To find the empirical formula, we need to divide the number of moles of each element by the smallest number of moles.
Moles of carbon in empirical formula = Moles of carbon / Moles of carbon
= 0.07 mol / 0.07 mol
= 1
Moles of hydrogen in empirical formula = Moles of hydrogen / Moles of carbon
= 0.08 mol / 0.07 mol
≈ 1.14
- The ratio of moles suggests that there are approximately 1 carbon atom and 1.14 hydrogen atoms in the empirical formula.
- Since we cannot have a fraction of an atom, we round the number of hydrogen atoms to the nearest whole number, which is 1.
Therefore, the empirical formula of the hydrocarbon is C1H1, which can be simplified to CH.
Conclusion:
The empirical formula of the gaseous hydrocarbon is C1H1 or CH.
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