Carminic acid,a naturally occuring red pigment extracted from the cochineal insect, contains only C,H,and O. 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 of the 0.3602 g sample pf the carminic acid requires 18.02 Ml of 0.0406 M NaOH to neutralize. Assuming there is only 1 acidic hydrogen per molecule, what is the molecular formula of carminic acid?

I know that carminic acid is a monoprotic acid and that I have to find the empirical formula fist then the gram molar weight, but how do I set this problem up in order to solve it? Do I add up the given percentages and then subtract them from 100% to find the percent of O?

yes on the given percentages, get the empirical formula first. Now determine the mass of the OH, and the moles OH in the base, that is the m oles of H in the acid.

thanks, this is very helpful!

Yes, to find the percent of oxygen (O), you can subtract the percentages of carbon (C) and hydrogen (H) from 100%. Given that carminic acid contains only C, H, and O and that it is 53.66% C and 4.09% H by mass, you can calculate the percent of O as follows:

Percent O = 100% - Percent C - Percent H
Percent O = 100% - 53.66% - 4.09%
Percent O = 42.25%

Now, once you have the percentages of C, H, and O, you can assume a 100-gram sample of carminic acid, which means you have 53.66 grams of C, 4.09 grams of H, and 42.25 grams of O.

Next, you need to convert these masses into moles. To do this, divide each mass by its molar mass:

Number of moles of C = mass of C / molar mass of C
Number of moles of H = mass of H / molar mass of H
Number of moles of O = mass of O / molar mass of O

The molar mass of C is 12.01 g/mol, the molar mass of H is 1.008 g/mol, and the molar mass of O is 16.00 g/mol.

Once you have the number of moles for each element, you need to find their mole ratio by dividing each number of moles by the smallest number of moles. This will give you the empirical formula of carminic acid.

Finally, to determine the molecular formula of carminic acid, you need additional information about its molecular weight. Since the molecular formula will be an integer multiple of the empirical formula, you need to calculate the molar mass of the empirical formula and divide it into the given molar mass to obtain the molecular formula.

To determine the empirical formula of carminic acid, you need to calculate the number of moles of each element based on the given percentages of carbon (C) and hydrogen (H). Once you find the empirical formula, you can determine the molecular formula by comparing its molar mass to the given mass of the compound.

Let's start by assuming we have 100 g of carminic acid, which will allow us to calculate the mass of each element in the compound:

Mass of C = 53.66 g
Mass of H = 4.09 g

Now, we can convert the mass of each element into moles using their atomic masses:

Molar mass of C = 12.01 g/mol
Molar mass of H = 1.01 g/mol

Moles of C = Mass of C / Molar mass of C
= 53.66 g / 12.01 g/mol
≈ 4.468 mol

Moles of H = Mass of H / Molar mass of H
= 4.09 g / 1.01 g/mol
≈ 4.05 mol

Next, we need to find the mole ratio of C and H to simplify the empirical formula. We divide both moles by the smaller value (in this case, 4.05 mol):

Moles of C (simplified) = 4.468 mol / 4.05 mol
≈ 1.102 mol

Moles of H (simplified) = 4.05 mol / 4.05 mol
= 1 mol

Now, we can calculate the mass of oxygen (O) by subtracting the sum of the masses of C and H from the total mass of the compound:

Mass of O = Total mass of compound - (Mass of C + Mass of H)
= 100 g - (53.66 g + 4.09 g)
= 42.25 g

The percent composition of O can then be calculated:

Percent of O = (Mass of O / Total mass of compound) × 100%
= (42.25 g / 100 g) × 100%
= 42.25%

So, the empirical formula of carminic acid contains approximately 1.102 moles of C, 1 mol of H, and 0.4225 moles of O.

Now, to determine the molecular formula, we need to know the molar mass of carminic acid. We can do this by comparing the given mass of the sample (0.3602 g) to its molar mass.

Molar mass of carminic acid = Given mass of sample / Moles of carminic acid
= 0.3602 g / (1.102 mol C + 1 mol H + 0.4225 mol O)

Now you can calculate the molar mass of carminic acid and compare it to the known molar masses of organic compounds to deduce its molecular formula.