Question

A 3.4 g sample of an unknown monoprotic organic acid composed of C,H, and O is burned in air to produce 8.58 grams of carbon dioxide and 1.50 grams of water vapor. It was also determined that 279 mL of 0.1 M KOH was needed to titrate the acid completely.

Answer 1

`C_7H_6O_2`

Step-by-step explanation:

Hello there!

In this case, we can divide the problem in three stages: (1) determine the empirical formula with the combustion analysis, (2) compute the molar mass of acid via the moles of the acid in the neutralization and (3) determine the molecular formula.

(1) In this case, since 8.58 g of carbon dioxide are released, we can first compute the moles of carbon in the compound:

`n_C=8.58gCO_2*(1molCO_2)/(44.01gCO_2)*(1molC)/(1molCO_2)=0.195molC`

And the moles of hydrogen due to the produced 1.50 grams of water:

`n_H=1.50gH_2O*(1molH_2O)/(18.02gH_2O)*(2molH)/(1molH_2O) =0.166molH`

Next, to compute the mass and moles of oxygen, we need to use the initial 3.4 g of the acid:

`m_O=3.4g-0.195molC*(12.01gC)/(1molC)-0.166molH*(1.01gH)/(1molH) =0.89gO\\\\n_O=0.89gO*(1molO)/(16.0gO)=0.0556molO`

Thus, the subscripts in the empirical formula are:

`C=(0.195)/(0.0556)=3.5 \\\\H=(0.166)/(0.0556)=3\\\\O=(0.0556)/(0.0556)=1\\\\C_7H_6O_2`

As they cannot be fractions.

(2) In this case, since the acid is monoprotic, we can compute the moles by multiplying the concentration and volume of KOH:

`n_(KOH)=0.279L*0.1mol/L\\\\n_(KOH)=0.0279mol`

Which are equal to the moles of the acid:

`n_(acid)=0.0279mol`

And the molar mass:

`MM_(acid)=(3.4g)/(0.0279mol) =121.86g/mol`

(3) Finally, since the molar mass of the empirical formula is:

7*12.01 + 6*1.01 + 2*16.00 = 122.13 g/mol

Thus, since the ratio of molar masses is 122.86/122.13 = 1, we infer that the empirical formula equals the molecular one:

`C_7H_6O_2`

Best regards!