Question

Dalton's Law of Partial Pressures can be used to simplify gas stoichiometry problems. As a derivative of the ideal gas law, Dalton's Law assumes that gas particles are featureless little billiard balls, bouncing off each other and the walls of their container. Because of the assumption of ideality, 20 moles of helium, a mixture of 16 moles of nitrogen and 4 moles of oxygen, or a mixture of 10 moles of water vapor, 8 moles of carbon dioxide, and 2 moles of sulfur dioxide all produce the same total pressure and occupy the same volume.

#) A miniature volcano can be made in the laboratory with ammonium dichromate. When ignited, it decomposes in a fiery display according to the following balanced equation:

(NH4)2Cr2O7 (s) → N2 (g) + 4 H2O (g) + Cr2O3 (s)

1. a) What is the total number of moles of gas produced by one mole of reaction? (2 points)

   Careful: chromium (III) oxide is a crystalline ionic solid. It occupies practically no volume at all and exerts no significant pressure on the walls of its container.

2. b) What is ratio of total moles of gas produced to moles of ammonium dichromate reacted?

   Total moles gas produced Moles gas

Moles ammonium dichromate reacted '= Moles (NH4)2Cr2O7

c) What is the ratio of moles of nitrogen produced to total moles of gas produced? This value is called the “mole fraction of nitrogen” in the product mixture of gases.

Moles of nitrogen gas produced '= Moles N2 gas Total moles of gas produced Total moles of gas

d) What is the ratio of moles of water vapor produced to total moles of gas produced? This value is called the “mole fraction of water vapor” in the product mixture of gases.

Moles of water vapor produced '= Moles H2O vapor Total moles of gas produced Total moles of gas

Answer 1

Solution :-

Balanced reaction equation.

(NH4)2Cr2O7 (s) → N2 (g) + 4 H2O (g) + Cr2O3 (s)

Part a) As we can see in the balanced reaction equation, when 1 mole of solid reactant ammonium dichromate reacts then it produces 1 mole of nitrogen gas and 4 moles of water vapor so the total number of moles of gases produced are 1+4 = 5 mol gas

So total 5 moles of gas are produced.

Part b) ratio of the total moles of gas produced to the moles of ammonium dichromate

Moles of gases produced / moles of ammonium dichromate

5 mol / 1 mol = 5

So the ratio is 5

Part c) mole fraction of nitrogen = moles of nitrogen / total moles of gases

                                                            = 1 mol N2 / 5 mol gases

                                                             = 0.20

Therefore the mole fraction of the nitrogen is 0.20

Part d) mole fraction of water vapor = moles of water vapor / total moles of gases

                                                                  = 4 mol / 5 mol

                                                                  = 0.80

Therefore mole fraction of the water vapor is 0.80