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The relative activity of a species i, denoted a i, is defined [4] [5] as: = where μ i is the (molar) chemical potential of the species i under the conditions of interest, μ o i is the (molar) chemical potential of that species under some defined set of standard conditions, R is the gas constant, T is the thermodynamic temperature and e is the exponential constant.
Gay-Lussac used the formula acquired from ΔV/V = αΔT to define the rate of expansion α for gases. For air, he found a relative expansion ΔV/V = 37.50% and obtained a value of α = 37.50%/100 °C = 1/266.66 °C which indicated that the value of absolute zero was approximately 266.66 °C below 0 °C. [12]
The driving force shown here as ' ' is expressed in units of moles per unit of volume, but in some cases the driving force is represented by other measures of concentration with different units. For example, the driving force may be partial pressures when dealing with mass transfer in a gas phase and thus use units of pressure.
Stoichiometry is not only used to balance chemical equations but also used in conversions, i.e., converting from grams to moles using molar mass as the conversion factor, or from grams to milliliters using density. For example, to find the amount of NaCl (sodium chloride) in 2.00 g, one would do the following:
How much gas is present could be specified by giving the mass instead of the chemical amount of gas. Therefore, an alternative form of the ideal gas law may be useful. The chemical amount, n (in moles), is equal to total mass of the gas (m) (in kilograms) divided by the molar mass, M (in kilograms per mole): =.
As a more complex example, the concentration of nitrogen oxides (NO x) in the flue gas from an industrial furnace can be converted to a mass flow rate expressed in grams per hour (g/h) of NO x by using the following information as shown below: NO x concentration = 10 parts per million by volume = 10 ppmv = 10 volumes/10 6 volumes NO x molar mass
The generalized force for a system known to be in energy eigenstate is given by: X = − d E r d x {\displaystyle X=-{\frac {dE_{r}}{dx}}} Since the system can be in any energy eigenstate within an interval of δ E {\displaystyle \delta E} , we define the generalized force for the system as the expectation value of the above expression:
The enthalpy of fusion is the amount of energy required to convert one mole of solid into liquid. For example, when melting 1 kg of ice (at 0 °C under a wide range of pressures), 333.55 kJ of energy is absorbed with no temperature change. The heat of solidification (when a substance changes from liquid to solid) is equal and opposite.