How many carbon atoms are in 44g H2C2O4?

Answer 1

The molar mass of this compound is 58 g. Hence 44g amounts to .7586 moles.

One mole of this compound contains 2 x N₀ (where N₀) is the Avagadro number) of carbon atoms.

This works out be be 9.133 x 10²³

Answer 2

Hi Clarie,

This is a classic question that calls for dimensional analysis. That means we will use a series of conversions to change from one unit – the given mass [M] in grams – to a desired unit – quantity [N] of atoms.

Master dimensional analysis as a tool to use on many different types of chemistry problems.

It's important that we determine a clear path from our givens to what we want to calculate, i.e., our desired dimension or unit.

First, we analyze the solution steps we'll need to break down the mass of a compound into its individual atoms, specifically the quantity of its carbon atoms.

CONCEPTS TO REVIEW:

To convert a mass to a quantity of objects, we use the concept of the mole and Avogadro's number 6.022*10²³. A mole of any compound is 6.022*10²³ molecules of that compound.

The atomic mass values found in the periodic table are also the molar masses of those elements, e.g., 1 mole of H atoms = 1.008 g H.

DETERMINE SOLUTION PATH:

We sketch a solution path so we know our start and end points:

1) Start at the far left with the given amount of the compound – 44g H₂C₂O₄ (oxalic acid)

2) At the far right, write your end goal – # of atoms

3) Determine the conversion factors needed:

– grams to moles of cmpd

– moles of compound (cmpd) to moles of carbon in the cmpd

– moles of carbon to # of carbon atoms

We write conversion factors as ratios of numbers and units with fraction lines, such as: 1 mol / 6.022 *10²³ atoms. We must include units and substances, such as moles of C.

Conversion factors below are in parentheses.

4) Our solution path is:

44g H₂C₂O₄ * (moles cmpd / grams cmpd) * (moles C / moles cmpd) * (# of C atoms / moles C) = # of atoms of C

5) Before filling in number values, we check the units to ensure they cancel appropriately. Note the final unit is in the numerator of the final conversion factor.

Example to check units:

44g H₂C₂O₄ * (mol H₂C₂O₄ / g H₂C₂O₄)

Correct, because grams are in both the numerator and denominator, so they will cancel, leaving moles.

6) Converting grams (mass of cmpd) to moles (number of molecules of the cmpd) requires the molar mass. Look up the molar mass of each element in the substance using the periodic table.

I suggest an interactive table such as this one from Fisher Scientific:

www.fishersci.com/us/en/periodic-table.html

Molar mass:

H₂C₂O₄ = (1.008 g H /mol)*2 + (12.01 g C/mol)*2 + (16.00 g O/mol)*4

= 90.036 g/mol H₂C₂O₄

7) Add numerical values to path:

44g H₂C₂O₄ * (1 mol H₂C₂O₄ / 90.036 grams H₂C₂O₄) * (2 mol C / 1 mol H₂C₂O₄) * (6.022 *10²³ C atoms / 1 mol C) = # of C atoms

(1 mol H₂C₂O₄ / 90.036 grams) means 1 mole of oxalic acid has a mass of 90.036 grams, calculated from its 3 constituent elements H, C, and O.)

(2 mol C / 1 mol cmpd) means 2 moles of C in every 1 mol of cmpd.

8) Cancel units:

g H₂C₂O₄

mol H₂C₂O₄

mol C

Check final unit: C atoms.

9) Multiple and divide values:

44 * (1 / 90.036 ) * (2 / 1 ) * (6.022 *10²³ / 1 )

= 5.886*10²³ C atoms

10) Check significant figures. Original problem: 2 SFs.

Answer: 5.9*10²³ C atoms.