A compound having an empirical formula of #C_3H_4O_3# has a mass of 180 g/mol. What is the molecular formula?

Question

Wyatt Atkins · Accepted Answer

#"Molecular formula"# #=# #C_6H_8O_6#

The empirical formula and the molecular formula are always multiples of whole numbers:

i.e. #"Molecular formula"# #=# #"(Empirical formula)"xxn#

So we need to solve for #n#.

Thus #180*g*mol^-1# #=# #nxx(3xx12.011+4xx1.0079+3xx15.999)*g*mol^-1# #=# #nxx(88.0)*g*mol^-1#

#n~=2#. Thus #"Molecular formula"# #=# #C_6H_8O_6#.

Naturally, there is a small error in the ratio; these kinds of errors are common when determining formulas of this kind.

Jose Ayala · Answer

undefined To find the molecular formula from the empirical formula, you need to compare the molar mass of the empirical formula with the given molecular mass.

First, calculate the molar mass of the empirical formula:
(3*12.01) + (4*1.008) + (3*16.00) = 36.03 + 4.032 + 48.00 = 88.062 g/mol

Then, divide the given molecular mass by the molar mass of the empirical formula to find the multiplier:
180 g/mol / 88.062 g/mol ≈ 2.045

Finally, multiply the subscripts in the empirical formula by the multiplier to get the molecular formula:
C3H4O3 * 2 ≈ C6H8O6

So, the molecular formula is C6H8O6.