Instruction

1

Imagine that the inquisitive king Hieron gave his courtier math another crown and ordered: "Here, they're pure gold. Define Archimedes, what is the concentration of

**molecules**in it." A brilliant scientist such a task would put in an impasse. Well, you solve it very quickly. Suppose a crown weighed exactly 1.93 kg occupying a volume of 100 cm^3.2

First of all, find how many moles of gold are contained in such amount of substance. Using the periodic table you will learn

**molecules**arnow mass of gold: 197.e.m. (atomic mass units). And the mass of one mole of any substance (in grams) is numerically equal to its**molecules**arnoi weight. Therefore, one mole of gold weighs 197 grams. Dividing the actual weight of the crown on the molar mass of gold, you will receive: 1930/197 = of 9.79. Or, in round figures, of 9.8 moles of gold.3

Multiply the number of moles on the universal Avogadro's number showing how many elementary particles contained in a mole of any substance. 9,8*6,022*10^23 = 5,9*10^24. That's how many

**molecules**of gold is approximately contained in the crown.4

Well, now to find

**the concentration****of molecules**easier. 100 cubic centimetres – it is 0.0001 m^3. Divide: 5,9*10^24/0,0001 = 5,9*10^28. The concentration**of the molecules**of gold are equal to 5.9*10^28/m3.5

Now suppose that you are given such a task: if the pressure P, the mean square speed

**of molecules**of carbon dioxide equal to V. it is Required to determine**the concentration of**its**molecules**. And there is nothing complicated. There are so-called basic equation of kinetic theory of ideal gas: P = V^2m0C/3, where C is the concentration**of molecules**of gas, and m0 is the mass of one**molecules of**s. Therefore, the required concentration of C is: C = 3P/m0V^2.6

The only unknown value m0. It can be found in the Handbook of chemistry and physics. You can also calculate by the formula: m0 = M/Na where M is the molar mass of carbon dioxide (44 g/mol) and Na is Avogadro's number (6,022х1023). Substituting all values into the formula, calculate the required

**concentration of**S.7

Will modify the condition of the problem. Suppose you know only the temperature T and pressure P of carbon dioxide. How can I use these data to find

**the concentration of**its**molecules**? The pressure and temperature of gas are related by the formula: P = CkT, where C is the concentration**of molecules**of gas, K – Boltzmann constant equal to 1.38*10^-23. That is, C = P/kT. Substituting in the formula the known values, you calculate**the concentration of**S.