# Collisions and Concentration

For two molecules to react, they must first come into contact with each other. This contact can be considered a "collision." The more mobile the molecules are, the more likely they are to collide. In addition, the closer the molecules are together, the more likely they are to collide.

In the following drawings, the molecules are closer together in the picture on the right than they are in the picture on the left. The molecules are more likely to collide and react in the picture on the right. The two figures above might be described in terms of population density. Both drawings appear to offer the same amount of space, but are inhabited by different amounts of molecules. The difference is much like the difference between human population densities in various locations around the world. Some places, such as Mexico City or Tokyo, are very crowded; they have high population densities. Some places, such as the Australian Outback or the Canadian Arctic, have low population densities.

### Problem RK5.1.

In which location are you more likely to bump into another person: the Upper East Side of New York City or 75 degrees north, 45 degrees west, Greenland?

### Problem RK5.2.

Rank the following places in terms of population density (the number of people per square kilometer).

1. Russia: pop. 143 million; area 17 million km2
2. Bahrain: pop. 1.2 million; area 750 km2
3. Argentina: pop. 41 million; area 2.7 million km2
4. China: pop. 1.3 billion; area 9.6 million km2
5. Malawi: pop. 15 million; area 118 thousand km2
6. Vatican City: pop. 850; area 0.44 km2
7. Jamaica: pop. 2.7 million; area 10,990 km2

Sometimes many people are living in a small area, and the population density is high. Sometimes, the population is large, but the area is, too. Population density depends on two different factors: the number of people and the area in which they are spread out.

Concentration is the term we use to describe the population density of molecules (and other chemical entities such as atoms or ions). It describes the number of molecules there are, but also how much space, or volume, they have to move around. Thus, whereas a human population density may be described in terms of people per square kilometer, the concentration of a solution may be described in terms of molecules per liter.

### Problem RK5.4.

In the cases above, describe what would happen to rates of collisions between molecules right to left in the drawings.

### Problem RK5.5.

1. In the following drawings, state what is happening to the concentration of molecules of each type from left to right. 1. Explain what would happen to the rate of collisions between red molecules and blue molecules from left to right.
2. How would the answer about rates change if the situation here were reversed: if the number of blue molecules stayed the same and the number of red molecules increased?
3. How would the answer about rates change if the numbers of both the red and the blue molecules were increasing at the same time?

Scientists do not often account for individual molecules in a solution. It is more convenient to deal with groups of molecules, because individual molecules are too small to work with. In dealing with molecules in bulk, chemists usually use a unit called a mole, often abbreviated to mol. It is a numerical quantity, the same type of unit as a "dozen." Molecules are easier to keep track of by the mole, rather than individually.

### Problem RK5.6.

1. In the following solutions, how many dozen blue molecules are there in each case?
2. What is happening to the concentration from one beaker to the next? Quantify your answer. In reality, molecules and even moles of molecules are not counted. When working with a compound, it is weighed out on a balance. The known weight of the compound can then be used to determine the number of moles.

To measure out molecules by weight, the precise weight of each molecule must be known. For example: in the figure below, suppose equal numbers of red and blue molecules are required, and a red molecule weighs three times as much as a blue molecule. Three times as much red must be weighed out, compared with blue. ### Problem RK5.7.

You are developing a new "extreme sport" amusement park ride. Each ride (for one person) is powered by one mouse and one elephant. You have plenty of elephants to get started, but will need to go and buy some mice.

1. If an elephant weighs 6,800 kg, how many grams does it weigh?
2. If you have 47,600 kg of elephants, how many rides can you set up?
3. If a mouse weighs 25 g, how many g of mice will you need to buy?
4. Suppose you decide to get three extra mice (sometimes accidents happen around elephants). What is the total weight of mice you would need, including these extras?

### Problem RK5.8.

Suppose each of the following beakers contains an equal weight of each kind of molecule. The molecular weight of a blue molecule is 60 g/mol. What is the molecular weight of a red, an orange and a grey molecule? The weight of a molecule can be determined by adding up the weights of all its atoms. For example, a carbon dioxide molecule has a molecular weight of 44 amu (carbon is 12 amu plus two oxygens at 16 amu apiece). The weight of a mole of carbon dioxide is the same as the molecular weight, but in grams instead of amu. A mole of carbon dioxide is 44 g. In other words, the molecular weight (MW) of carbon is 44 g/mol.

### Problem RK5.9.

How much does a mole of each of the following molecules weigh?

1. nitric oxide, NO2
2. glucose, C6H12O6
3. benzaldehyde, C7H6O
4. phosphorus pentoxide, P2O5

### Problem RK5.10.

How many moles of each of the following compounds are there in the given weights?

1. 3 grams of glucose
2. 10 grams of benzaldehyde
3. 30 grams of phosphorus pentoxide

### Problem RK5.11.

What is the concentration of each of the following solutions (in moles per liter)?

1. 5 g of glucose in 50 mL of water
2. 11 g of benzaldehyde in 25 mL of THF
3. 9 g of menthol (MW 156 g/mol) in 60 mL of DMF