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Q.

What is the formula of normality? How do I calculate normality?

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Detailed Solution

Chemistry Formulas

Formula NameFormulaVariablesApplication
NormalityN = (Number of gram equivalents of solute) / (Volume of solution in L)

N = Normality

Gram equivalents = Mass/Equivalent weight

Used to express concentration of solutions in acid-base and redox reactions
Normality (Alternative)N = M × n

N = Normality

M = Molarity

n = Number of equivalents

Converting molarity to normality
MolarityM = (Number of moles of solute) / (Volume of solution in L)

M = Molarity

Moles = Mass/Molar mass

Most common concentration unit
Molalitym = (Number of moles of solute) / (Mass of solvent in kg)

m = Molality

Mass of solvent in kg

Temperature-independent concentration
Equivalent WeightEquivalent Weight = Molecular Weight / ValencyValency = Number of replaceable H⁺ or OH⁻ ionsUsed in normality calculations

Statistics Formulas

Formula NameFormulaVariablesApplication
Normal Distribution (PDF)f(x) = (1/(σ√(2π))) × e^(-½((x-μ)/σ)²)

f(x) = Probability density

μ = Mean

σ = Standard deviation

x = Variable

Describes bell-shaped probability distribution
Standard Normal DistributionZ = (X - μ) / σ

Z = Standard normal variable

X = Original variable

μ = Population mean

σ = Population standard deviation

Converting to standard normal form
Normal Distribution (CDF)Φ(z) = ∫_{-∞}^z (1/√(2π)) × e^(-t²/2) dt

Φ(z) = Cumulative probability

z = Standard normal variable

Finding probabilities under normal curve

Physics Formulas

Formula NameFormulaVariablesApplication
Normal Force (Horizontal Surface)N = mg

N = Normal force

m = Mass

g = Acceleration due to gravity

Force perpendicular to surface
Normal Force (Inclined Plane)N = mg cos θθ = Angle of inclinationObject on inclined surface
Normal Stressσ = F / A

σ = Normal stress

F = Applied force

A = Cross-sectional area

Stress perpendicular to surface
Normal Strainε = ΔL / L₀

ε = Normal strain

ΔL = Change in length

L₀ = Original length

Deformation per unit length

Mathematics Formulas

Formula NameFormulaVariablesApplication
Vector Normalizationû = u / ||u||

û = Unit vector

u = Original vector

||u|| = Magnitude of vector

Creating unit vectors
L2 Normalizationx_norm = x / √(Σx²)

x_norm = Normalized value

x = Original value

Σx² = Sum of squares

Data preprocessing in machine learning
Min-Max Normalizationx_norm = (x - x_min) / (x_max - x_min)

x_norm = Normalized value

x_min = Minimum value

x_max = Maximum value

Scaling data to [0,1] range
Normal Vector to Linen⃗ = (A, B) for line Ax + By + C = 0

n⃗ = Normal vector

A, B = Coefficients

Perpendicular vector to line
Normal Vector to Planen⃗ = (A, B, C) for plane Ax + By + Cz + D = 0

n⃗ = Normal vector

A, B, C = Coefficients

Perpendicular vector to plane

Economics Formulas

Formula NameFormulaVariablesApplication
Normal ProfitNormal Profit = Total Revenue - (Explicit Costs + Implicit Costs)When Normal Profit = 0, firm earns exactly its opportunity costBreak-even point in economics
Economic ProfitEconomic Profit = Total Revenue - Total Opportunity CostTotal Opportunity Cost includes both explicit and implicit costsTrue economic performance measure
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