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QUESTION

# What is the theoretical yield of sodium chloride for the reaction of 36.0 g Na with 75.2 g Cl2 of the following 2NA+Cl2---&gt; 2NaCl? I keep getting stuck with my conversions. I started with 36.0g NA (1 mol Na/22.99g Na) (1 mol Cl2/2mol Na) =0.782 mol Cl2....

The theoretical yield is 91.5g of NaCl

Method 1

Start with the equation:

2Na_((s))+Cl_(2(g))rarr2NaCl_((s))

So 2 mole Na reacts with 1 mole Cl_2 to give 2 molesNaCl

Convert moles to grams: A_r Na=23 A_rCl=35.5

2x23 = 46g Na reacts with 2x 35.5 = 71g  Cl_2 to give 2x(23 +35.5 ) = 117g NaCl

Use simple proportion to find how much would be made from 36g Na by first working out what 1 g of Na would give by dividing through by 46:

(46/46)g Na reacts with (71/46) g Cl_2 to give (117/46)g NaCl

So:

1g Na reacts with 1.54g Cl_2 to give 2.54g NaCl

So:

36g Na reacts with 1.54x36= 55.44g Cl_2 to give 2.54x36=91.44g NaCl

You can see that the chlorine is in excess so the theoretical yield is 91.5g of NaCl to 1sf.

Method 2

Start with the balanced equation as above. Calculate the amount of NaCl that can form from each reactant.

36.0 g Na × "1 mol Na"/"22.99 g Na" × "2 mol NaCl"/"2 mol Na" = 1.566 mol NaCl (3 significant figures + 1 guard digit)

75.2 g Cl₂ × ("1 mol Cl"_2)/("70.91 g Cl"_2) × "2 mol NaCl"/("1 mol Cl"_2) = 2.121 mol NaCl

The Na gives fewer moles of NaCl, so Na is the limiting reactant.

The theoretical yield is

1.566 mol NaCl × "58.44 g NaCl"/"1 mol NaCl" =" 91.5 g NaCl"

Method 3

Divide the moles of each reactant by its coefficient in the balanced equation.

36.0 g Na × "1 mol Na"/"22.99 g Na" =" 1.566 mol Na" (3 significant figures + 1 guard digit)

75.2 g Cl₂ × ("1 mol Cl"_2)/("70.91 g Cl"_2) =" 2.121 mol Cl"_2

2"Na" + "Cl"_2 → 2"NaCl"

1.566/2; 2.121/1

0.7829; 2.121

NaCl gives fewer "moles of reaction", so NaCl is the limiting reactant.

So theoretical yield is

0.7829 mol reaction × "2 mol NaCl"/"1 mol reaction" × "58.44 g NaCl"/"1 mol NaCl" = 91.5 g NaCl

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