Stoichiometry: finding the yield in reaction of sodium azide with iron oxide

[pc2-brazil]

Thank you in advance.

Homework Statement

Nitrogen gas can be obtained from the reaction between sodium azide and iron oxide.

$$6NaN_3_{(s)}+Fe_2O_3_{(s)} \rightarrow 3Na_2O_{(s)}+2Fe_{(s)}+9N_2_{(g)}$$

a) What is the yield of this reaction, knowing that, from 390 g of azide and 400 g of iron oxide, 100 g of metalic iron were produced?

b) What is the volume (in litres = L) of N₂ produced, in a pression of 0.82 atm and a temperature of 27^oC, in the conditions given in item a?

Universal constant of gases = R = 0.082 (atm L)/(mol K).

Homework Equations

$$PV = nRT$$ (P = atm, V = litres, n = mol, R = universal constant of gases, T = Kelvin).

The Attempt at a Solution

a) First, the molar relation between sodium azide and iron oxide, in order to discover what is the limiting reactant:

Mass of 6NaN₃ = 6(23 + 3(16)) = 6(23 + 48) = 6(65) = 390 g.
Mass of Fe₂O₃ = 2(56) + 3(16) = 112 + 48 = 160 g.
Mass of 2Fe = 2(56) = 112 g.
$$6 mol NaN_3 \rightarrow 1 mol Fe_2O_3$$
$$390 g NaN_3\rightarrow 160 g Fe_2O_3$$

Since we already have 390 g of NaN₃, a rule of three will not be necessary.
This mass of sodium azide produces 160 g of iron oxide; thus, there is excess of iron oxide. Therefore, the limiting reactant is NaN₃.

Mass of metalic iron produced:
$$6 mol NaN_3 \rightarrow 2 mol Fe$$
$$390 g \rightarrow 112 g$$
The mass of metalic iron is 112g. Since the problem states the mass produced is 100 g, dividing 100 / 112 will give the yield (R):
$$R = \frac{100}{112}$$
R equals approximately 89.2%.

b) Convert 27^oC to Kelvin = 27 + 273 = 300 K.
To find the molar volume (V_m): $$PV_m = nRT$$, then $$0.82V_m = 0.082 \times 300$$; thus V_m = 30 L.
Since 390 g of NaN₃ equal 6 mol, then the volume of N₂ produced is 9V_m.
$$V = 9V_m = 9 \times 30 = 270 L$$
But the yield is 89.2%:
$$V = 0.892 \times 270$$
V equals 240.82 L.

 

[Borek]

a OK, for b I got a little bit more. Not much. Don't round down intermediate results.

 

[pc2-brazil]

a OK, for b I got a little bit more. Not much. Don't round down intermediate results.

Thank you for the response. This calculation was done by hand (100/112 = 50/58 = 25/28 = ~89,2). The next digit would be 8, which makes difference in the result (270 * 89.28 = 271.056). Anyway, if we were to do the calculation of the volume like this:
$$V = \frac{100 \times 270}{112} = \frac{25 * 270}{28} = \frac{25 * 135}{14}$$
the result would be better.
It is very good to know that the reasoning to solve the problem is right.

 

[Borek]

It is possible that part of the difference is in molar masses, I am using my stoichiometry calculator and it does all calculations using as exact molar masses as possible.