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QuestionA 48.71 g iron sample reacts with sulfur to form a 90.67 g metal sulfide. Find the empirical formula (Fe, S).

Studdy Solution

STEP 1

Assumptions1. The mass of the iron sample is48.71 g. . The mass of the metal sulfide formed is90.67 g.
3. The sulfur is in excess, meaning all of the iron is used up in the reaction.
4. The empirical formula is the simplest, most reduced ratio of elements in a compound.

STEP 2

First, we need to find the mass of sulfur in the metal sulfide. We can do this by subtracting the mass of the iron from the mass of the metal sulfide.
Mass of ulfur=Mass of metal sulfide−Mass of IronMass\, of\,ulfur = Mass\, of\, metal\, sulfide - Mass\, of\, Iron

STEP 3

Now, plug in the given values for the mass of the metal sulfide and the mass of the iron to calculate the mass of sulfur.
Mass of ulfur=90.67 g−48.71 gMass\, of\,ulfur =90.67\, g -48.71\, g

STEP 4

Calculate the mass of sulfur.
Mass of ulfur=90.67 g−48.71 g=41.96 gMass\, of\,ulfur =90.67\, g -48.71\, g =41.96\, g

STEP 5

Now, we need to convert the mass of each element to moles. We can do this by dividing the mass of each element by its molar mass. The molar mass of iron (Fe) is55.845 g/mol and the molar mass of sulfur () is32.06 g/mol.
Moles of Fe=Mass of FeMolar mass of FeMoles\, of\, Fe = \frac{Mass\, of\, Fe}{Molar\, mass\, of\, Fe}Moles of =Mass of Molar mass of Moles\, of\, = \frac{Mass\, of\,}{Molar\, mass\, of\,}

STEP 6

Plug in the values for the mass of iron and sulfur and their molar masses to calculate the moles of each element.
Moles of Fe=48.71 g55.845 g/molMoles\, of\, Fe = \frac{48.71\, g}{55.845\, g/mol}Moles of =41.96 g32.06 g/molMoles\, of\, = \frac{41.96\, g}{32.06\, g/mol}

STEP 7

Calculate the moles of each element.
Moles of Fe=48.71 g55.845 g/mol=0.872 molMoles\, of\, Fe = \frac{48.71\, g}{55.845\, g/mol} =0.872\, molMoles of =41.96 g32.06 g/mol=1.308 molMoles\, of\, = \frac{41.96\, g}{32.06\, g/mol} =1.308\, mol

STEP 8

To find the empirical formula, we need to find the simplest whole number ratio of moles of each element. We do this by dividing each number of moles by the smallest number of moles calculated.
Ratio of Fe=Moles of FeSmallest number of molesRatio\, of\, Fe = \frac{Moles\, of\, Fe}{Smallest\, number\, of\, moles}Ratio of =Moles of Smallest number of molesRatio\, of\, = \frac{Moles\, of\,}{Smallest\, number\, of\, moles}

STEP 9

Plug in the values for the moles of each element and the smallest number of moles to calculate the ratio of each element.
Ratio of Fe=.872 mol.872 molRatio\, of\, Fe = \frac{.872\, mol}{.872\, mol}Ratio of =.308 mol.872 molRatio\, of\, = \frac{.308\, mol}{.872\, mol}

STEP 10

Calculate the ratio of each element.
Ratio of Fe=0.872 mol0.872 mol=Ratio\, of\, Fe = \frac{0.872\, mol}{0.872\, mol} =Ratio of =.308 mol0.872 mol=.5Ratio\, of\, = \frac{.308\, mol}{0.872\, mol} =.5

STEP 11

Since we can't have half of an atom in an empirical formula, we need to multiply all ratios by to get a whole number ratio.
Ratio of Fe=times=Ratio\, of\, Fe = \\times =Ratio of =.5times=3Ratio\, of\, =.5 \\times =3The empirical formula of the metal sulfide is Fe3.

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