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A chemistry student is given an unknown compound and is asked to identify its molecular formula using mass spectrometry. The compound has a molecular ion peak at m/z 86 and fragments at m/z 43 and 58. What is the molecular formula of the unknown compound?

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To determine the molecular formula of the unknown compound, we can start by examining the molecular ion peak at m/z 86. This peak represents the mass-to-charge ratio of the intact molecule. Since most molecules have a charge of +1 in mass spectrometry, we can assume that the molecular weight of the compound is 86.Next, we can look at the fragment peaks at m/z 43 and 58. These peaks represent the masses of fragments produced when the molecule breaks apart during the mass spectrometry process. By analyzing these fragments, we can gain insight into the structure and composition of the original molecule.To determine the molecular formula, we can start by considering the most common elements found in organic compounds: carbon  C , hydrogen  H , oxygen  O , and nitrogen  N . We can then use the molecular weight of 86 to calculate the possible combinations of these elements that would result in a molecular weight of 86.For example, a molecular formula of C4H10O would have a molecular weight of  4 x 12  +  10 x 1  +  1 x 16  = 48 + 10 + 16 = 74, which is not equal to 86. Therefore, we can rule out this possibility.After trying various combinations, we find that the molecular formula C4H10O2 has a molecular weight of  4 x 12  +  10 x 1  +  2 x 16  = 48 + 10 + 32 = 90, which is close to the molecular ion peak at m/z 86. However, we should also consider the possibility of other elements, such as halogens, being present in the compound.A molecular formula of C3H6O2Br would have a molecular weight of  3 x 12  +  6 x 1  +  2 x 16  +  1 x 79  = 36 + 6 + 32 + 79 = 153, which is too high. However, if we consider the presence of chlorine  Cl , we find that the molecular formula C3H6O2Cl has a molecular weight of  3 x 12  +  6 x 1  +  2 x 16  +  1 x 35  = 36 + 6 + 32 + 35 = 109, which is still too high.After further analysis, we find that the molecular formula C3H7NO2 has a molecular weight of  3 x 12  +  7 x 1  +  1 x 14  +  2 x 16  = 36 + 7 + 14 + 32 = 89, which is very close to the molecular ion peak at m/z 86. This molecular formula is consistent with the fragment peaks at m/z 43 and 58, which could represent the loss of a neutral fragment with a mass of 43 or 28, respectively.Therefore, the most likely molecular formula for the unknown compound is C3H7NO2.

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