# Question 1b7d3

Jun 15, 2015

The molecular formula is $\text{C"_6"H"_8"O"_6}$.

#### Explanation:

We need to determine the empirical formula and the empirical formula mass. Then divide the molecular mass by the empirical mass, then multiply the empirical formula times the result.

EMPIRICAL FORMULA

Determine the masses
The percentages given add up to $\text{100.00%}$. In a $\text{100 g}$ sample, the masses would be the percentages in grams.

$\text{C"="40.92 g}$
$\text{H"="4.58 g}$
$\text{O"="54.50 g}$

Determine the molar masses of the elements (atomic weight in g/mol).

$\text{C"="12.0107 g/mol}$
$\text{H"="1.00794 g/mol}$
$\text{O"="15.999 g/mol}$

Determine the number of moles of each element from the given mass and the molar mass.

$\text{C} :$$40.92 \cancel{\text{g C"xx(1 "mol C")/(12.010 cancel"g C")="3.407 mol C}}$

$\text{H} :$ $4.58 \cancel{\text{g H"xx(1 "mol H")/(1.00794 cancel"g H")="4.54 mol H}}$

$\text{O} :$ $54.50 \cancel{\text{g O"xx(1 "mol O")/(15.999 cancel"g O")="3.406 mol O}}$

Determine mole ratios by dividing the moles for each element by the smallest number of moles.

$\text{C} :$ $\left(3.407 \text{mol")/(3.406 "mol}\right) = 1.000$

$\text{H} :$ $\left(4.54 \text{mol")/(3.406 "mol}\right) = 1.33$

$\text{H} :$ $\left(3.406 \text{mol")/(3.406 "mol}\right) = 1.000$

Multiply the ratios times $3$ to get all whole numbers.

$\text{C} :$ $1.000 \times 3 = 3.000$
$\text{H} :$ $1.33 \times 3 = 3.99$
$\text{O} :$ $1.000 \times = 3.000$

The empirical formula is ${\text{C"_3"H"_4"O}}_{3}$.
The empirical formula mass = (3xx12.0107"g/mol")+(4xx1.00794"g/mol")+(3xx15.999"g/mol")=88.061"g/mol"

MOLECULAR FORMULA

Divide molecular mass by empirical mass. Multiply the empirical formula times the result.

$\text{Molecular mass"/"empirical mass" = "176.1 g/mol"/"88.061 g/mol} = 2.000$

Molecular formula $=$ $\text{C"_3"H"_4"O"_3}$ times 2 $=$${\text{C"_6"H"_8"O}}_{6}$

Jun 15, 2015

Here's an alternative technique you can use to get the molecular formula.

#### Explanation:

If you know the percent composition and the molar mass of a compound, here's how you can determine its molecular formula.

A compound's molar mass tells you what the exact mass of 1 mole of that compound is. In your case, you know that ascorbic acid has a molar mass of 176.1 g/mol.

This means that 1 mole of ascorbic acid has a total mass of 176.1 g. Let's assume that you have a 176.1-g sample of ascorbic acid. According to ascorbic acid's percent composition, every 100 g of acid will contain 40.92 g carbon, 4.58 g hydrogen, and 54.50 g oxygen.

This means that your 176.1-g sample will contain

176.1cancel("g") * "40.92 g C"/(100cancel("g")) = "72.06 g C"

176.1cancel("g") * "4.58 g H"/(100cancel("g")) = "8.065 g H"

176.1cancel("g") * "54.50 g"/(100cancel("g")) = "95.97 g O"

To get the number of moles each element contributes to 1 mole of ascorbic acid, simply divide these numbers by each element's molar mass

"For C": (72.06cancel("g"))/(12.0cancel("g")/"mol") = 6.005 ~= 6

"For H": (8.065cancel("g"))/(1.01cancel("g")/"mol") = 7.985 ~= 8

"For O": (95.97cancel("g"))/(16.0cancel("g")/"mol") = 5.998 ~= 6#

Therefore, the molecular formula of ascorbic acid is

${C}_{6} {H}_{8} {O}_{6}$

One mole of ascorbic acid contains 6 moles of carbon, 8 moles of hydrogen, and 6 moles of oxygen.