# 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?

Jul 3, 2016

You need 121 g of ${\text{TiCl}}_{4}$.

#### Explanation:

1. Write the balanced equation

The balanced equation is

${\text{TiCl"_4 + "2Mg" → "Ti" + "2MgCl}}_{2}$

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.

$\text{Theoretical yield" = 25.0 color(red)(cancel(color(black)("g actual"))) × "100 g theoretical"/(82 color(red)(cancel(color(black)("g actual"))))= "30.5 g theoretical}$

We must plan to get 30.5 g of $\text{Ti}$ to produce an actual yield of 25.0 g.

3. Calculate the moles of $\text{Ti}$

$\text{Moles of Ti" = 30.5 color(red)(cancel(color(black)("g Ti"))) × "1 mol Ti"/(47.87 color(red)(cancel(color(black)("g Ti")))) = "0.637 mol Ti}$

4. Calculate the moles of ${\text{TiCl}}_{4}$

${\text{Moles of TiCl"_4 = 0.637 color(red)(cancel(color(black)("mol Ti"))) × ("1 mol TiCl"_4)/(1 color(red)(cancel(color(black)("mol Ti")))) = "0.637 mol TiCl}}_{4}$

5. Calculate the mass of ${\text{TiCl}}_{4}$

${\text{Mass of TiCl"_ 4 = 0.637 color(red)(cancel(color(black)("mol TiCl"_4))) × "189.68 g TiCl"_4/(1 color(red)(cancel(color(black)("mol TiCl"_4)))) = "121 g TiCl}}_{4}$