Chemistry Question

Question

Potassium nitrate is widely used as a fertilizer because it provides two essential elements, potassium and nitrogen. It is made by mixing potassium chloride and nitric acid in the presence of oxygen according to the equation

4KCl(aq) + 4HNO₃(aq) + O₂(g) --> 4KNO₃(aq) + 2Cl₂(g) + 2H₂O(I)     

How many kilograms of potassium nitrate will be produced from a solution containing 49.8 kg of potassium chloride and one containing 47 kg of nitric acid?  

Answer 1

The balance chemical reaction equation:

4KCl(aq) + 4HNO₃(aq) + O₂(g) → 4KNO₃(aq) + 2Cl₂(g) + 2H₂O(I)

is in units of moles (4 moles of KCl mix with 4 moles of HNO₃ and 1 mole of O₂ to produce 4 moles of KNO₃, 2 moles of Cl₂, and 2 moles of H₂O) so the first step is converting the mass into moles using the molar mass:

Step 1 - Calculate molar mass:

• potassium chloride = KCl

K = 39.098 g/mol x 1 = 39.098

Cl = 35.453 g/mol x 1 = 35.453

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74.551 g/mol

• nitric acid = HNO3

H = 1.008 g/mol x 1 = 1.008

N = 14.007 g/mol x 1 = 14.007

O = 15.999 g/mol x 3 = 47.997

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63.012 g/mol

• potassium nitrate = KNO₃:

K = 39.098 g/mol x 1 = 39.098

N = 14.007 g/mol x 1 = 14.007

O = 15.999 g/mol x 3 = 47.997

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101.102 g/mol

Step 2 - Calculate moles from mass:

For KCL (potassium chloride):

49.8 kg x 1000g/1kg = 49800 g

(49800 g)/(74.551 g/mol) = 667.999 moles

For HNO₃ (nitric acid):

47 kg x 1000g/1kg = 47000 g

(47000 g)/(63.012 g/mol) = 745.890 moles

Step 3 - Calculate moles of KNO₃:

Notice that in the chemical reaction equation, we need an equal number of moles of KCL and HNO₃ so the fact that there is more of the HNO3 doesn't help. We will only be using 667.999 moles of those 745.890 available. The rest is excess and will not be consumed in the reaction. Consequently, we say that KCl is the limiting reactant.

Also notice that the chemical reaction equation says there are 4 moles of KNO₃ produced from 4 moles of KCL and 4 moles of HNO₃. So, since we are using 667.999 moles of the 2 reactants, we will get 667.999 moles of KNO₃

Step 4 - Calculate mass of KNO₃:

(667.999 moles) x (101.102 g/mol) = 67536 g

67536 g x 1 kg/1000g = 67.536 kg

Round to 3 sig figs since you started with 49.8 kg KCl (the 47 kg of HNO3 didn't get used in the calculation) so the mass of KNO₃ produced is 67.5 kg