What is the limiting reactant in a Grignard reaction?

EXAMPLE

Assume that, in a preparation of triphenylmethanol, you prepared phenylmagnesium bromide by reacting 2.1 mL of bromobenzene (density 1.50 g/mL) with 0.50 g of magnesium in anhydrous ether. To this, you then slowly added a solution of 2.4 g benzophenone in anhydrous ether. What was the limiting reactant?

Solution

The equations (#"Ph" = "C"_6"H"_5#) are:

#"PhBr" + "Mg" → "PhMgBr"#
#"Ph"_2"C=O" + "PhMgBr" → "Ph"_3"COMgBr"#
#"Ph"_3"COMgBr" + "H"^+ → "Ph"_3"COH" + "Mg"^(2+) + "Br"^"-"#

Calculate the moles of each reactant

#2.1 color(red)(cancel(color(black)("mL PhBr"))) × (1.50 color(red)(cancel(color(black)("g PhBr"))))/(1 color(red)(cancel(color(black)("mL PhBr")))) × "1 mol PhBr"/(157.0 color(red)(cancel(color(black)("g PhBr")))) = "0.020 mol PhBr"#

#0.50 color(red)(cancel(color(black)("g Mg"))) × "1 mol Mg"/(24.30 color(red)(cancel(color(black)("g Mg")))) = "0.021 mol Mg"#

#2.4 color(red)(cancel(color(black)("g Ph"_2"CO"))) × ("1 mol Ph"_2"CO")/(182.2 color(red)(cancel(color(black)("g Ph"_2"CO")))) = "0.013 mol Ph"_2"CO"#

Identify the limiting reactant

All theoretical molar ratios are 1:1.

Since benzophenone has the fewest moles, it is the limiting reactant.