Determine the empirical formula of a compound containing 47. 37 grams of carbon, 10. 59 grams of hydrogen, and 42. 04 grams of o
1 answer:
Considering the definition of empirical formula, the empirical formula is C₃H₈O₂ and the molecular formula is C₉H₂₄O₆.
<h3>Definition of empirical formula</h3>The empirical formula is the simplest expression to represent a chemical compound, which indicates the elements that are present and the minimum proportion in whole numbers that exist between its atoms, that is, the subscripts of chemical formulas are reduced to the most integers. small as possible.
<h3>Empirical formula in this case</h3>In this case, you have:
- Carbon (C): 47.37 grams
- Hydrogen (H): 10.59 grams
- Oxygen (O): 42.04 grams
Then it is possible to calculate the number of moles of each atom in the molecule, taking into account the corresponding molar mass:
- Carbon (C):
= 3.95 moles
- Hydrogen (H):
= 10.59 moles
- Oxygen (O):
= 2.63 moles
The empirical formula must be expressed using whole number relationships, for this the numbers of moles are divided by the smallest result of those obtained. In this case:
- Carbon (C):
= 1.5
- Hydrogen (H):
= 4
- Oxygen (O):
= 1
Finally, since in the empirical formula the numbers of moles must be expressed in whole numbers, the ratio of atoms is multiplied by some number with which everything is obtained in simple whole numbers (in this case by 2):
- Carbon (C): 1.5× 2= 3
- Hydrogen (H): 4× 2= 8
- Oxygen (O): 1× 2= 2
Therefore the C: H: O mole ratio is 3: 8: 2
Finally, the empirical formula is C₃H₈O₂.
<h3>Molecular formula</h3>To obtain the molecular formula you must relate its molecular weight (PMc) with the molecular weight of the empirical formula (PMfe).
PMfe= PM (C₃H₈O₂)= 76 g/mole
The molar mass of the compound (PMc) was determined to be 228.276 g/mol. Dividing this mass PMc by the molar mass of the empirical formula PMfe gives:
228.276 g/mol ÷ 76 g/mole= 3
This means that in the molecular formula there are 3 unit formulas (empirical formulas), so it is necessary to multiply the number of all atoms by 3.
Then, the molecular formula is C₉H₂₄O₆.
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Using conditional probability, it is found that there is a 0.052 = 5.2% probability that a randomly chosen U. S. President is left-handed and a democrat.
<h3>What is Conditional Probability?</h3>Conditional probability is the probability of one event happening, considering a previous event. The formula is:
In which
- P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
- P(A) is the probability of A happening.
In this problem, the events are:
- Event A: President is left-handed.
- Event B: President is a democrat.
Researching the problem on the internet, it is found that:
- 40% of the presidents were left-handed, hence P(A) = 0.4.
- If a president is left-handed, there is a 13% chance that the president is a Democrat, hence P(B|A) = 0.13.
Then:
0.052 = 5.2% probability that a randomly chosen U. S. President is left-handed and a democrat.
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