What mass of #TiCl_4# is needed to produce 25.0 g of #Ti# if the reaction proceeds with an 82% yield in the reaction #TiCl_4 + 2Mg -> Ti + 2MgCl_2#?

1 Answer
Jul 3, 2016

Answer:

You need 121 g of #"TiCl"_4#.

Explanation:

1. Write the balanced equation

The balanced equation is

#"TiCl"_4 + "2Mg" → "Ti" + "2MgCl"_2#

2. Calculate the theoretical amount of Ti

An 82 % yield means that we get 82 g of product from a theoretical value of 100 g.

#"Theoretical yield" = 25.0 color(red)(cancel(color(black)("g actual"))) × "100 g theoretical"/(82 color(red)(cancel(color(black)("g actual"))))= "30.5 g theoretical"#

We must plan to get 30.5 g of #"Ti"# to produce an actual yield of 25.0 g.

3. Calculate the moles of #"Ti"#

#"Moles of Ti" = 30.5 color(red)(cancel(color(black)("g Ti"))) × "1 mol Ti"/(47.87 color(red)(cancel(color(black)("g Ti")))) = "0.637 mol Ti"#

4. Calculate the moles of #"TiCl"_4#

#"Moles of TiCl"_4 = 0.637 color(red)(cancel(color(black)("mol Ti"))) × ("1 mol TiCl"_4)/(1 color(red)(cancel(color(black)("mol Ti")))) = "0.637 mol TiCl"_4#

5. Calculate the mass of #"TiCl"_4#

#"Mass of TiCl"_ 4 = 0.637 color(red)(cancel(color(black)("mol TiCl"_4))) × "189.68 g TiCl"_4/(1 color(red)(cancel(color(black)("mol TiCl"_4)))) = "121 g TiCl"_4#