Question

C and H elemental analysis of a compound Z gives \(88.2 \% \mathrm{C}, 11.8 \% \mathrm{H} .\) An exact mass determination using high-resolution mass spectrometry gives a mass of \(68.06260 .\) In the low-resolution mass spectrum, the major peaks that are observed are at \(m / z=68,67,53,41,40,39\) and \(26 .\) Show that these data are consistent with \(\mathbf{Z}\) being \(1,3-\) pentadiene \((\mathbf{1 0} . \mathbf{1 3})\).

Short answer

The data confirms \(Z\) is 1,3-pentadiene \(\text{C}_5\text{H}_8 \), matching the empirical formula and mass spectrometry data.

Step-by-step solution

Calculate Empirical Formula

The elemental composition given is 88.2% C and 11.8% H. For a sample of 100 g, this corresponds to 88.2 g of carbon and 11.8 g of hydrogen.Calculate the moles of each element:- Moles of C = \( \frac{88.2}{12.01} = 7.34 \) moles- Moles of H = \( \frac{11.8}{1.008} = 11.71 \) molesDetermine the simplest whole number ratio by dividing each by the smallest number of moles (7.34):- C:H ratio = \( \frac{7.34}{7.34} : \frac{11.71}{7.34} = 1 : 1.6 \)Multiplying by the smallest number to obtain whole numbers gives approximately C5H8.

Verify Molar Mass with High Resolution Data

The empirical formula C5H8 has a molar mass calculated as follows:- Molar Mass = \( 5 \times 12.01 + 8 \times 1.008 = 68.11 \) g/mol.This is consistent with the given exact mass of 68.06260 obtained from high-resolution mass spectrometry, confirming that the empirical formula is likely the molecular formula.

Analyze Low Resolution Mass Spectrum Data

The low-resolution mass spectrum has major peaks at \( m/z = 68, 67, 53, 41, 40, 39, \text{and} 26 \).- \( m/z = 68 \): Likely corresponds to the molecular ion \( \text{C}_5\text{H}_8^+ \).- \( m/z = 67 \): Possibly a fragment resulting from the loss of H atom \( \text{C}_5\text{H}_7^+ \).- Other peaks can be explained as fragments resulting from further cleavage or rearrangements in the molecule.

Confirm Identity as 1,3-Pentadiene

Given the molecular formula \( \text{C}_5\text{H}_8 \) and the peak analysis, identify the structure as 1,3-pentadiene. This is supported by its capability to form the observed mass spectrum fragments, likely due to common cleavage patterns in dienes.

Key concepts

Elemental Analysis

Elemental analysis is a technique to determine the composition of a compound by mass of each element it contains. In our exercise, the compound was analyzed and found to consist of 88.2% carbon (C) and 11.8% hydrogen (H). These percentages tell us the mass of each element in 100 grams of the compound. Therefore, we have 88.2 grams of carbon and 11.8 grams of hydrogen, which are essential in calculating the empirical formula.

The next step involves converting these masses to moles using the atomic masses (often found on the periodic table). This is done because moles relate to the actual number of atoms, providing a more meaningful ratio for chemical formulas.

• Moles of Carbon, C = \( \frac{88.2}{12.01} = 7.34 \) moles
• Moles of Hydrogen, H = \( \frac{11.8}{1.008} = 11.71 \) moles

Through these calculations, we link the macroscopic properties of the compound to its microscopic structure, paving the way to discover its empirical and molecular formulas.

Empirical Formula Calculation

To find the empirical formula, which represents the simplest whole-number ratio of elements in a compound, we divide the number of moles of each element by the smallest number of moles calculated in the analysis. In this case, the smallest number of moles is that of carbon, 7.34 moles.

• Ratio of Carbon to Hydrogen = \( \frac{7.34}{7.34} : \frac{11.71}{7.34} = 1 : 1.6 \)

Since empirical formulas must contain whole numbers, we need to multiply the ratio by a number that will convert 1.6 to a whole number. Multiplying both parts of the ratio by approximately 3 gives:

• 1.6 × 3 = 4.8, which rounds to 5
• Therefore, empirical formula = \( \text{C}_5\text{H}_8 \)

Thus, the empirical formula conveys that for every 5 carbon atoms, there are 8 hydrogen atoms. This reflects the basic unit of the compound's structure in the simplest terms possible.

Molecular Formula Determination

The molecular formula tells the actual number of each type of atom in a molecule, and in many cases, it matches the empirical formula. We verify this by comparing the calculated molar mass of the empirical formula with the exact mass provided by high-resolution mass spectrometry (HRMS).

The empirical formula \( \text{C}_5\text{H}_8 \) gives a molar mass calculated as follows:

• Carbon (C): \( 5 \times 12.01 = 60.05 \)
• Hydrogen (H): \( 8 \times 1.008 = 8.064 \)
• Total molar mass = 60.05 + 8.064 = 68.11 g/mol

The exact mass determined by HRMS is 68.06260, very close to our calculated value, confirming \( \text{C}_5\text{H}_8 \) as the molecular formula. This step ensures that our understanding aligns with precise measurements, validating our conclusions.

Mass Spectrum Interpretation

Interpreting a mass spectrum involves understanding the fragmentation pattern of a molecule. The mass spectrum for our compound shows major peaks at different m/z (mass-to-charge) ratios which reveal information about the structure and fragments of the molecule.

- The peak at \( m/z = 68 \) likely represents the molecular ion \( \text{C}_5\text{H}_8^+ \).- A peak at \( m/z = 67 \) may be due to the loss of a hydrogen atom, resulting in the fragment \( \text{C}_5\text{H}_7^+ \).- Other smaller peaks like 53, 41, 40, 39, and 26 indicate possible further breaks and rearrangements of the molecule.

These interpretations help to verify the existence and structure of possible molecular configurations, such as 1,3-pentadiene, evidenced by typical patterns seen in dienes. Understanding these fragments aids in confirming the structural integrity and identity of the compound.