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Normality can be used for acid-base titrations. For example, sulfuric acid (H 2 SO 4) is a diprotic acid. Since only 0.5 mol of H 2 SO 4 are needed to neutralize 1 mol of OH −, the equivalence factor is: f eq (H 2 SO 4) = 0.5. If the concentration of a sulfuric acid solution is c(H 2 SO 4) = 1 mol/L, then its normality is 2 N. It can also be ...
The parameters μ and 1/ are analogous to μ and σ 2 (the mean and variance) in the normal distribution: μ is a measure of location (the distribution is clustered around μ), and; is a measure of concentration (a reciprocal measure of dispersion, so 1/ is analogous to σ 2).
Diagram showing the cumulative distribution function for the normal distribution with mean (μ) 0 and variance (σ 2) 1. These numerical values "68%, 95%, 99.7%" come from the cumulative distribution function of the normal distribution.
In analytical chemistry, a solution of any substance which contains one equivalent per litre is known as a normal solution (abbreviated N), so the example sodium hydroxide solution would be 0.0893 N. [3] [13] The relative uncertainty (u r) in the measured concentration can be estimated by assuming a Gaussian distribution of the measurement ...
The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when μ = 0 {\textstyle \mu =0} and σ 2 = 1 {\textstyle \sigma ^{2}=1} , and it is described by this probability density function (or density): φ ( z ) = e − z 2 2 2 π . {\displaystyle \varphi (z ...
Solutions that can be formally expanded in this way are known as normal solutions to the Boltzmann equation. [6] This class of solutions excludes non-perturbative contributions (such as /), which appear in boundary layers or near internal shock layers. Thus, Chapman–Enskog theory is restricted to situations in which such solutions are negligible.
The Avogadro constant, commonly denoted N A [1] or L, [2] is an SI defining constant with an exact value of 6.022 140 76 × 10 23 mol −1 (reciprocal moles). [3] [4] It is this defined number of constituent particles (usually molecules, atoms, ions, or ion pairs—in general, entities) per mole and used as a normalization factor in relating the amount of substance, n(X), in a sample of a ...
A different technique, which goes back to Laplace (1812), [3] is the following. Let = =. Since the limits on s as y → ±∞ depend on the sign of x, it simplifies the calculation to use the fact that e −x 2 is an even function, and, therefore, the integral over all real numbers is just twice the integral from zero to infinity.