Every object in the universe attracts every other object with a force (gravitational force FG) directed along the line through centres of the two objects that is proportional to the product of their masses and inversely proportional to the square of the distance between them.
m1 and m2 are masses of the two objects and r is the distance between them. G is universal constant of gravitation, which equals 6.67•10-26 N m2 kg-2. Strictly speaking, this law applies only to objects that can be considered pointlike object. Otherwise, the force has to be found by integrating the forces between various mass elements.
It is more properly to express Newton’s gravitational law by vector equation:
in which r1 and r2 are position vectors of masses m1 and m2.
Gravitational forces act on distance. Newton’s gravitational law is derived from Kepler’s law for planetary motion, using a physical assumption considering Sun as the centre and the source of gravitational force.
Additionally, every object moves in the direction of the force acting on it, with acceleration that is inversely proportional to the mass of object. For bodies on the surface of Earth, the distance r in gravitational law formula is practically equal to the Earth radius, RE. If the mass of the body on Earth surface is m and the mass of earth is ME, the gravitational force acting on that body can be expressed as:
where g is gravitational acceleration which is, although dependent on geographical latitude, usually considered as constant equal to 9.81 m s-2.
Practical salinity SP is defined on the Practical Salinity Scale of 1978 (PSS-78) in terms of the conductivity ratio K15 which is the electrical conductivity of the sample at temperature t68 = 15 °C and pressure equal to one standard atmosphere, divided by the conductivity of a standard potassium chloride (KCl) solution at the same temperature and pressure. The mass fraction of KCl in the standard solution is 0.0324356 (32.4356 g of KCl in 1 kg of solution). When K15 = 1, the Practical Salinity P S is by definition 35. The conductivity of that reference solution is C(35,1568,0) = 42.914 mS/cm = 4.2914 S/m (Siemens per meter). Note that Practical Salinity is a unit-less quantity. Though sometimes convenient, it is technically incorrect to quote Practical Salinity in "psu". When K15 is not unity, SP and K15 are related by the PSS-78 equation
At a temperature of t68 = 15 °C, Rt is simply K15 and Practical Salinity SP can be determined from the above equation. For temperatures other than t68 = 15 °C, Practical Salinity SP is given by the following function of Rt (k = 0.0162)
Second-order reaction is a reaction with a rate law that is proportional to either the concentration of a reactant squared, or the product of concentrations of two reactants.
For a general unimolecular reaction,
The reaction rate expression for a second order reaction is
If assumed that the concentration of reactant A is [A]o at t=0 and [A] at time T, the variables in the rate equation and integrate can be separated. The integrated rate law for a second-order reaction can be easily shown to be
Solubility product constant (Ksp) (or the solubility product) is the product of the molar concentrations of the constituent ions, each raised to the power of its stoichiometric coefficient in the equilibrium equation. For instance, if a compound AaBb is in equilibrium with its solution
the solubility product is given by
Stoichiometric coefficient (ν) is the number appearing before the symbol for each compound in the equation for a chemical reaction. By convention, it is negative for reactants and positive for products.
Stoichiometric coefficients describe the stoichiometry of the chemical reaction.
In this equation, a, b, c and d are called as Stoichiometric coefficients of the A, B, C and D respectively.
Hardness is defined as the concentrations of calcium and magnesium ions expressed in terms of calcium carbonate. These minerals in water can cause some everyday problems. They react with soap and produce a deposit called soap curd that remains on the skin and clothes and, because it is insoluble and sticky, cannot be removed by rinsing.
Hard water may also shorten the life of plumbing and water heaters. When water containing calcium carbonate is heated, a hard scale is formed that can plug pipes and coat heating elements. Scale is also a poor heat conductor. With increased deposits on the unit, heat is not transmitted to the water fast enough and overheating of the metal causes failure. Build-up of deposits will also reduce the efficiency of the heating unit, increasing the cost of fuel.
There are two types of water hardness, temporary and permanent.
Temporary Hardness is due to the bicarbonate ion, HCO3-, being present in the water. This type of hardness can be removed by boiling the water to expel the CO2, as indicated by the following equation:
Permanent hardness is due to calcium and magnesium nitrates, sulphates, and chlorides etc. This type of hardness cannot be eliminated by boiling.
Water supply classification | |
---|---|
Hardness | Concentration of Calcium carbonate (mg/L) |
Soft Water | 0 to 75 |
Medium Hard Water | 75 to 150 |
Hard Water | 150 to 300 |
Very Hard Water | over 300 |
The Lennard-Jones potential (or 12-6 potential) is a mathematically simple model that describes the interaction between two non-bonded and uncharged atoms (known as the van der Waals interaction). It was first proposed in 1924 by British physicist Sir John Edward Lennard-Jones (1894-1954). The Lennard-Jones Potential is given by the following equation
V(r) = 4e[(sigma/r)12-(sigma/r)6)]where V is the intermolecular potential between the two atoms or molecules, ε is the well depth and a measure of how strongly the two particles attract each other, σ is the distance at which the intermolecular potential between the two particles is zero, r is the distance of separation between centres of both particles.
Generalic, Eni. "Ilkovic equation." Croatian-English Chemistry Dictionary & Glossary. 29 June 2022. KTF-Split. {Date of access}. <https://glossary.periodni.com>.
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