Analyze

Our approach will require several steps: (1) Use the combustion data to determine the percent composition of the compound (similar to Example 3-6). (2) Determine the empirical formula from the percent composition (similar to Example 3-5). (3) Obtain the molecular formula from the empirical formula and the molecular mass. (4) Determine how the C, H, and O atoms represented in the molecular formula might be assembled into a dicarboxylic acid. Use molar masses with (at least) one more significant figure than in the measured masses where possible; store intermediate results in your calculator without rounding off.

Solve

1. Determine the percent composition. Calculate the mass of H in 1.629 g H_{2}O          ? g H = 1.629 g H_{2}O × \frac{1  mol  H_{2}O}{18.015  g  H_{2}O} × \frac{2  mol  H}{1  mol  H_{2}O} × \frac{1.008  g  H}{1  mol  H} = 0.1823 g H

and then the mass percent H in the 2.250 g sample of the dicarboxylic acid.          % H = \frac{0.1823  g  H}{2.250  g   compd.} × 100% = 8.102% H

Also, calculate the mass of C in 4.548 g CO_{2},          ? g C = 4.548 g CO_{2} × \frac{1  mol  CO_{2}}{44.009  g  CO_{2}} × \frac{1   mol  C}{1  mol  CO_{2}} × \frac{12.011  g  C}{1  mol  C} = 1.241 g C

followed by the mass percent C in the 2.250 g sample of dicarboxylic acid.          % C = \frac{1.241  g  C}{2.250  g  compd.} × 100% = 55.16% C

The mass percent O in the compound is obtained as a difference, that is,           % O = 100.00% − 55.16% C − 8 .102% H = 36.74% O

2. Obtain the empirical formula from the percent composition. The masses of the elements in 100.0 g of the compound are        55.16 g C   8.102 g H   36.74 g O

The numbers of moles of the elements in 100.0 g of the compound are            55.16 g C × \frac{1  mol  C}{12.011  g  C} = 4.592 mol C

8.102 g H × \frac{1  mol  H}{1.008  g  H} = 8.038 mol H

36.74 g O × \frac{1  mol  O}{15.999  g  O} = 2.296 mol O

The tentative formula based on these numbers is          C_{4.592}H_{8.038}O_{2.296}

Divide all the subscripts by 2.296 to obtain            C_{2}H_{3.50}O

Multiply all subscripts by two to obtain the empirical formula          C_{4}H_{7}O_{2}

and then determine the empirical formula mass.              (4 × 12.011 u) + (7 × 1.008 u) + (2 × 15.999 u) = 87.098 u

3. Obtain the molecular formula. The experimentally determined molecular mass of 174 u is twice the empirical formula mass. The molecular formula is            C_{8}H_{14}O_{4}

4. Assemble the atoms in C_{8}H_{14}O_{4} into a plausible structural formula. The dicarboxylic acid must contain two —COOH groups. This accounts for the two C atoms, two H atoms, and all four O atoms. The remainder of the structure is based on C_{6}H_{12}. For example, arrange the six —CH_{2} segments into a six-carbon chain and attach the —COOH groups at the ends of the chain.            HOOC—CH_{2}(CH_{2})_{4}CH_{2}—COOH

However, there are other possibilities based on shorter chains with branches, for example            HOOC—CH_{2}—\overset{\begin{matrix} CH_{3} \\ \mid \end{matrix} }{\underset{\begin{matrix} \mid \\ CH_{3} \end{matrix} }{C}}—CH_{2}—CH_{2}—COOH

Assess

We have found a plausible structural formula, but there are many other possibilities. For example, the following three isomers have a seven-carbon chain with one methyl group (—CH_{3}) substituted for an H atom on the chain:

In conclusion, we cannot identify a specific isomer with only the data given.