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Chapter 4: Problem 118

Carminic acid, a naturally occurring red pigment extracted from the cochineal insect, contains only carbon, hydrogen, and oxygen. It was commonly used as a dye in the first half of the nineteenth century. It is 53.66% C and 4.09% H by mass. A titration required 18.02 mL of 0.0406 M NaOH to neutralize 0.3602 g carminic acid. Assuming that there is only one acidic hydrogen per molecule, what is the molecular formula of carminic acid?

Short Answer

Expert verified
The molecular formula of carminic acid is \(C_8H_8O_4\).

Step by step solution

01

Convert mass percentages to moles

First, let's assume we have a 100g sample of Carminic acid. This way, the mass percentages become masses in grams, which we can convert to moles. Mass of Carbon (C) = 53.66 g Mass of Hydrogen (H) = 4.09 g Mass of Oxygen (O) = 100 g - 53.66 g - 4.09 g = 42.25 g Next, let's calculate the moles: Moles of C = (53.66 g) / (12.01 g/mol) = 4.4719 mol Moles of H = (4.09 g) / (1.008 g/mol) = 4.0563 mol Moles of O = (42.25 g) / (16.00 g/mol) = 2.6406 mol
02

Determine the empirical formula

Now let's find the ratio of moles of each element: Divide each value by the smallest number of moles: C = 4.4719 / 2.6406 = 1.694 H = 4.0563 / 2.6406 = 1.536 O = 2.6406 / 2.6406 = 1.000 Round off each ratio to the nearest whole number: C = 2 (approx) H = 2 (approx) O = 1 (approx) So, the empirical formula is approximately C2H2O.
03

Find the molar mass of the compound using titration data

Since the problem states that there is only one acidic hydrogen per molecule, the moles of acidic hydrogen in the sample are equal to the moles of NaOH used in the titration. Moles of NaOH = (0.0406 M) x (18.02 mL) x (1 L / 1000 mL) = 7.3209 x 10^-4 mol Since there is only one acidic hydrogen in C2H2O: Moles of carminic acid = moles of NaOH = 7.3209 x 10^-4 mol Now we can find the molar mass of carminic acid: Molar mass = mass of carminic acid / moles of carminic acid = (0.3602 g) / (7.3209 x 10^-4 mol) = 492.16 g/mol
04

Calculate the molecular formula

To find the molecular formula, we divide the molar mass of carminic acid by the molar mass of the empirical formula (C2H2O) and round off to the nearest whole number: Number of empirical formula units = (molar mass of carminic acid) / (molar mass of C2H2O) = 492.16 / (2*12.01 + 2*1.008 + 16) = 4 (approx) Multiply the empirical formula by this number to get the molecular formula: C2H2O * 4 = C8H8O4 Hence, the molecular formula of carminic acid is C8H8O4.

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Most popular questions from this chapter

You wish to prepare 1 L of a 0.02-M potassium iodate solution. You require that the final concentration be within 1% of 0.02 M and that the concentration must be known accurately to the fourth decimal place. How would you prepare this solution? Specify the glassware you would use, the accuracy needed for the balance, and the ranges of acceptable masses of \(\mathrm{KIO}_{3}\) that can be used

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