1)[10 points]

When Potassium Chlorate (KClO₃), is heated, it turns into Potassium Chloride (KCl) and Oxygen gas (O₂). The chemical equation that describes this reaction is:

2KClO₃ ----> 2KCl + 3O₂

(i.e. two molecules of KClO₃ produce two molecules of KCl and three molecules of O₂) Suppose 801.48 grams of pure KClO₃ are heated, liberating the oxygen as gas and leaving behind 487.66 grams of KCl. Assuming that the weight in "atomic mass units", amu, of atomic Oxygen is 16, calculate the weight in amu of KCl. Use only the information given above!

To check your answer, one can find from the periodic table that the weight of Potassium (K) is 39.09 amu, and the weight of Chlorine (Cl) is 35.45 amu.

2)[10 points]

A cylinder with a movable piston at one end contains a certain amount of ideal gas at a pressure p₁ and a volume V₁ at the temperature T₁=200°K. The pressure and the volume are then both doubled. What is now the final temperature in degrees Kelvin?

3)[10 points]

Suppose a deck of 52 cards are divided into two distinct piles according to the following scheme: each card has 50% chance to be place in either pile. What is the average number of cards in each pile? To a certainty of 99.99%, what is the range of number of cards that one might find in any one of the two piles. Give your answer in terms of the fraction of cards in one pile to the total number of cards 52.

10²³ molecules in a gas are confined to a container. Consider an imaginary partition that divides the container exactly into two halves of equal volume (the molecules may freely travel between the two halves). To 99.99% accuracy, what will be the range of possible numbers of molecules that will be found in any one half of the container? Give your answer in terms of the fraction of molecules in one half of the container compared to the total number of molecules 10²³.

(Hint: use the table on page 52 of the text, concerning the normal distribution.)