How to find the concentration of molecules

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.

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

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.

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.

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 ofs. Therefore, the required concentration of C is: C = 3P/m0V^2.

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.

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.