Given :
Volume of [tex]Fe^{2+}[/tex] , V = 132 mL .
Molarity of [tex]Fe^{2+}[/tex], M = 0.1782 M .
To Find :
How many milliliters of 0.2937 M [tex]K_2Cr_2O_7[/tex] are required to titrate 132.0 mL of 0.1782 M [tex]Fe^{2+}[/tex] solution .
Solution :
Moles of [tex]Fe_2[/tex] :
[tex]n=0.1782\times \dfrac{132}{1000}\ mol\\\\n=0.264\ mol[/tex]
Now , 1 mole of [tex]K_2Cr_2O_7[/tex] reacts with 6 mole of [tex]Fe^{2+}[/tex] .
So , moles of [tex]K_2Cr_2O_7[/tex] required is :
[tex]N=\dfrac{0.264}{6}=0.044\ mol[/tex]
Volume required is :
[tex]V=\dfrac{N}{M}\\\\V=\dfrac{0.044}{0.2937}\ L\\\\V=0.15\ L=150\ mL[/tex]
Hence , this is the required solution .