The Two-Column Method: Organizing an Attack on Chemistry Word-Problems

It is important to realize that not everyone thinks about or solves problems in the same way. Some people can read a problem and very quickly they have an idea or feeling about how they will reach their solution. Sometimes the most direct route to an answer is not so obvious and a little advanced planning makes things run more smoothly. In this example, we demonstrate the working of a problem via the two-column method, which is really just a way of organizing a plan of attack.

The problem is fairly complex and requires a number of logical and mathematical steps for its solution. We will walk you through the problem, along the way demonstrating how you might organize your approach using this two-column method. Of course, the first step is to read the problem, so here it is:

Question

• In the painting "The Discovery of Phosphorus" (shown) by the English painter Joseph Wright (1734-1797) an alchemist is depicted heating urine paste in a reaction vessel over coals. The brilliant light due to the reaction of phosphorus with oxygen is one of the products of the chemical reaction:
  
  P₄ (s) + n O₂ (g) P_xO_y (s) + light + heat.
  
  The resulting solid phosphorus oxide P_xO_y can then be treated with water to produce phosphoric acid according to the reaction:
  
  P_xO_y (s) + 6 H₂O (l) 4 H₃PO₄ (aq).
  
  You attempt to duplicate the first of these chemical reactions in a closed system. Your apparatus consists of a flask connected via tubing to a cylinder (with a frictionless, moveable piston-head seal) containing oxygen gas. The oxygen gas cylinder has graduated markings so you can observe the volume of oxygen gas inside of the cylinder. As oxygen is consumed in the reaction the piston head moves. For each mole of electrons removed from phosphorus, what change in volume do you observe in the oxygen cylinder? The density of oxygen gas at room temperature is 1.308 g/L. Assume that the gas cylinder is thermally insulated from the reaction vessel so the oxygen gas in the cylinder remains at room temperature.
  
  
  
  
  

General Comments

Solution Outline

Concepts Involved

First it may be a good idea to make a list of the concepts dealt with in the problem. You could either do this in your head or on paper.

1. Balancing Chemical Equations
2. Redox Reactions
3. Unit analysis (moles to liters, mole ratios, etc.)

The Outline of Steps

Start by listing the final desired quantity and how to get/why you want that quantity (in two separate columns). Then, in reverse order, list the steps you have to perform in order to get there. The last item in your list is your starting point. Essentially, we are making a reverse-outline of how we will solve the problem.

The Worked Solution

By balancing the second equation, it is determined that x = 4, y = 10:

P₄O₁₀ (s) + 6 H₂O (l) 4 H₃PO₄ (aq). [Note that there is no change in the oxidation state of phosphorus in this equation.]

With this information in hand, we can balance the first chemical equation and determine the number of moles of O₂ consumed per mole of P₄ reacted. We can also determine the oxidation states of all the elements in the balanced reaction.

P₄ (s) + 5 O₂ (g) P₄O₁₀ (s) + light + heat.

The oxidation numbers are P⁽⁰⁾ in P₄; O⁽⁰⁾ in O₂; P⁽⁺⁵⁾, O^(-2) in P₄O₁₀. Using the oxidation numbers and the stoichiometry in the balanced equation we know that there are 20 moles of electrons transferred to phosphorus atoms for every 5 moles of O₂ consumed. Now we have everything we need to execute the calculation and answer the question.