Question

Gadolinium oxide, a colorless powder which absorbs carbon dioxide from the air, contains 86.76 mass% Gd and 13.24% O. Determine its empirical formula (FW Gd=157.25, O=16.00) Please show work

Answer 1

If percentages are given, assume that the total mass is 100 grams so that

        the mass of each element = the percent given.

Gd = 86.76 g

O = 13.24 g

Convert the mass of each element to moles using the molar mass

86.76 g Gd * 1 mole Gd / 157.25 g = 0.5517 mole

13.24 g O * 1 mole O / 16 g = 0.8275 mole

Divide each mole value by the smallest number of moles calculated. Round to the nearest whole number.

0.5517 / 0.5517 mole Gd = 1

0.8275 / 0.5517 mole O = 1.5

This is the mole ratio of the elements and is represented by subscripts in the empirical formula.

If the number is too far to round (x.1 ~ x.9), then multiply each solution by the same factor to get the lowest whole number multiple.

1 Gd * 2 = 2Gd

1.5 O * 2 = 3O

Therefore empirical formula is Gd₂O₃