Titanium, a strong, lightweight metal used in many applications, is prepared by the reaction of titanium(IV) chloride with molten magnesium metal. 3.45 x 10^7g of titanium(IV) chloride is reacted with 1.13 x 10^7g of magnesium, 7.91 x 10^6g of titanium metal are obtained. What is the percent yield of the reaction?
This is a limiting reagent problem as well as a percent yield.
Write the balance equation.
Convert grams TiCl4 to moles. moles = grams/molar mass.
Do the same for Mg.
Using the coefficients in the balanced equation, convert moles of TiCl4 to moles of the product. Do the same for moles Mg. In is probably that the answer for moles Mg produced by the two procedures is not the same. In limiting regent problems the correct answer is ALWAYS the smaller value and the reagent producing that value is the limiting reagent. Convert the smaller value to grams by g = mols x molar mass.
Now percent yield = (g Ti produced/g Ti calculated above)*100.
To find the percent yield of the reaction, we need to compare the actual yield to the theoretical yield.
1. Calculate the molar mass of titanium(IV) chloride (TiCl4) and magnesium (Mg).
- The molar mass of TiCl4 = 47.87 g/mol (titanium) + (4 x 35.45 g/mol) (chlorine) = 189.69 g/mol.
- The molar mass of Mg = 24.31 g/mol.
2. Convert the given masses of titanium(IV) chloride and magnesium to moles.
- Moles of TiCl4 = (3.45 x 10^7 g) / (189.69 g/mol) = 182,097.44 mol.
- Moles of Mg = (1.13 x 10^7 g) / (24.31 g/mol) = 465,320.49 mol.
3. Determine the stoichiometric ratio between titanium(IV) chloride and titanium metal.
From the balanced equation of the reaction, we know that:
1 mol of TiCl4 reacts to produce 1 mol of Ti.
4. Calculate the theoretical yield of titanium metal in moles.
- Theoretical yield of Ti = moles of TiCl4 = 182,097.44 mol.
5. Convert the theoretical yield of titanium metal from moles to grams.
- Theoretical yield of Ti in grams = (182,097.44 mol) x (47.87 g/mol) = 8,715,453.9 g.
6. Calculate the percent yield of the reaction.
- Percent yield = (Actual yield / Theoretical yield) x 100.
- Actual yield of Ti = 7.91 x 10^6 g.
- Percent yield = (7.91 x 10^6 g / 8,715,453.9 g) x 100 = 90.65%.
Therefore, the percent yield of the reaction is approximately 90.65%.