Molecular Weight

Excerpts

• Molecular Weight

  Such a weight is called an *equivalent weight*. It is arbitrarily fixed for one element---generally for hydrogen at $1~\Unit{gr.}$---and then the equivalent weight of any other element (*e.g.* oxygen) is that weight which will combine with $1~\Unit{gr.}$ of hydrogen.

• Molecular Weight

  Hence, *equal volumes of perfect gases at the same temperature and pressure contain an equal number of molecules* (Avogadro’s law).

• Molecular Weight

  Hence half a molecule of hydrogen is called an atom of hydrogen, H; similarly, half a molecule of oxygen an atom of oxygen, O; and half a molecule of nitrogen an atom of nitrogen, N.

• Molecular Weight

  In the definition of the molecular weight as a quite definite quantity depending only on the particular state of a substance, and independent of possible chemical reactions with other substances, lies one of the most important and most fruitful achievements of theoretical chemistry.

• Molecular Weight

  In a word, we may, in a certain sense, say, that physical changes take place continuously, chemical ones, on the other hand, discontinuously. In consequence, the science of physics deals, primarily, with continuously varying numbers, the science of chemistry, on the contrary, with whole, or with simple rational numbers.

• Molecular Weight

  Thus $16$ parts by weight of oxygen combine with $28$ parts by weight of nitrogen to form nitrous oxide, or with $14$ parts to form % % nitric oxide, or with $9\frac{1}{3}$ parts to form nitrous anhydride, or with $7$ parts to form nitrogen tetroxide, or with $5\frac{3}{5}$ parts to form nitric anhydride.

• Molecular Weight

  The ambiguity is, however, removed by putting all these ratios $= 1$, *i.e.* by establishing the condition that equal volumes of different gases shall contain an equal number of equivalents.

• Molecular Weight

  Thus Avogadro’s law enables us to give in quite definite numbers the molecular quantities of each constituent present in the molecule of any chemically homogeneous gas, provided we know its density and its chemical composition.

• Molecular Weight

  which means that at a given temperature and pressure the volume of a quantity of gas depends only on the number of the molecules present, and not at all on the nature of the gas.

• Molecular Weight

  In doubtful cases it is safest, in general, to leave this question open, and to admit both chemical and physical changes as causes for the deviations from the laws of perfect gases.

• Molecular Weight

  The molecular weight of sulphur vapour below $800°$, for instance, % is generally assumed to be $\ce{S6} = 192$; but some assume a mixture of molecules $\ce{S8} = 256$ and $\ce{S2} = 64$, and others still different mixtures.

Equations

• Molecular Weight

  p = \frac{C_{0} \theta}{v_{0}}

  At a given temperature and pressure, hydrogen's pressure equals its constant C_0 times the temperature divided by its specific volume v_0.

• Molecular Weight

  p = \frac{C\theta}{v}

  For any other gas at the same temperature and pressure, the pressure equals its constant C times the temperature divided by its specific volume v.

• Molecular Weight

  C = \frac{m_{0}C_{0}}{m}

  The characteristic constant C of a gas is inversely proportional to its molecular weight m, scaled from the hydrogen constant C_0 and hydrogen molecular weight m_0 (equation 13).

• Molecular Weight

  C = \frac{m_{0}C_{0}}{m} = \frac{m_{0}}{m} · \frac{pv_{0}}{\theta} = \frac{2 · 1013650}{m · 273 · 0.00008988} = \frac{82600000}{m}

  Substituting the measured density of hydrogen at 0 °C and atmospheric pressure (with m_0 = 2) gives the characteristic constant C as approximately 82600000 divided by m.

• Molecular Weight

  82600000 = R

  The constant R is defined as the number 82600000 for brevity, and it is independent of the nature of the individual gas.

• Molecular Weight

  p = \frac{R}{m} · \frac{\theta}{v}

  The characteristic equation of a chemically homogeneous perfect gas of molecular weight m: pressure equals the absolute gas constant R divided by m, times temperature divided by specific volume (equation 14).

• Molecular Weight

  m = \frac{R}{C}

  The molecular weight of a gas can be deduced from its characteristic equation as the absolute gas constant divided by the characteristic constant C (equation 15).

• Molecular Weight

  v = \dfrac{V}{M}

  The specific volume v is the total volume V divided by the mass M of the gas.

• Molecular Weight

  V = \frac{R\theta}{p} · \frac{M}{m}

  The volume of a gas equals R times temperature over pressure, times the ratio of its mass to its molecular weight.

• Molecular Weight

  \dfrac{M}{m} = n

  The number of molecules n in a quantity of gas is defined as its mass M divided by its molecular weight m.

• Molecular Weight

  V = \frac{R\theta}{p} · n

  At given temperature and pressure, the volume of a quantity of gas depends only on the number of molecules n present, not on the nature of the gas.

• Molecular Weight

  p_{1} : p_{2} : \dots = C_{1}M_{1} : C_{2}M_{2}

  In a mixture, the ratio of the partial pressures of the constituent gases is the ratio of their characteristic constants times their masses (taken from equation 9).

• Molecular Weight

  p_{1} : p_{2} : \dots = \frac{M_{1}}{m_{1}} : \frac{M_{2}}{m_{2}} : \dots = n_{1} : n_{2} : \dots

  The ratio of the partial pressures of the gases in a mixture equals the ratio of the numbers of molecules of each gas present.

• Molecular Weight

  \frac{M_{1} + M_{2} + \dots}{m} = \frac{M_{1}}{m_{1}} + \frac{M_{2}}{m_{2}} + \dots

  The apparent molecular weight m of a mixture is defined so that the total mass divided by it equals the sum of the masses of each constituent divided by its molecular weight.

• Molecular Weight

  m = \frac{M_{1} + M_{2} + \dots}{\dfrac{M_{1}}{m_{1}} + \dfrac{M_{2}}{m_{2}} + \dots}

  The apparent molecular weight of a mixture is the total mass divided by the total number of molecules, which is the sum of each constituent's mass over its molecular weight.

• Molecular Weight

  \ce{C5H11Br} = \ce{C5H10 + HBr}

  The dissociation of amylene hydrobromide into amylene and hydrogen bromide, which doubles the number of molecules when the reaction is complete.

Problems

No exercises in this chapter.