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Differential Calculus

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Painting

Acid - Base Neutralization

(a) 12.5 ml of a 50 ml solution of sulphuric acid containing 0.490 g of sulphuric acid completely neutralized 20 ml of a sodium hydroxide solution during titration. Determine the concentration of the sodium hydroxide solution.

(b) The hydrochloric acid (HCl) concentration in the gastric juice of a patient with duodenal ulcer is 80 x 10^{-3} M. The patient produces 3 liters of gastric juice per day and his doctor has prescribed a medication containing 2.6 g Al(OH)_{3} per 100 ml of solution, for the relief of excess stomach acidity (Al(OH)_{3} and Mg(OH)_{2} are common ingredients in medications designed to neutralize stomach acid). Determine the patient's daily dose of the prescribed medication that will neutralize the acid.

**The strings**:

S_{7}P_{5}A_{52} (Change - Chemical Change).
**The math**:

Pj Problem of Interest is of type *change* (chemical change).

The chemical reaction of an *acid* with a *base* is called a *neutralization reaction*. *Salt* and *water* are the products of a neutralization reaction. For example, hydrochloric acid (HCl) reacts with sodium hydroxide (NaOH) in aqueous solution according to the following chemical equation:

HCl_{(aq)} + NaOH_{(aq)} -------> H_{2}O_{(l)} + NaCl_{(aq)}-------(1)

In reaction (1), the acidity of hydochloric acid is *neutralizaed*.
*Titration* is a laboratory procedure for determining the amount of one substance by determining the volume of a solution of known concentration of another substance that reacts completely with the first substance. *Titration* is commonly used in neutralization reactions to determine the amount of base that is chemically equivalent to a given amount of acid.

An *equivalent* is the molecular weight or mass of an acid or base that furnished one mole of protons (H^{+} or one mole of hydroxl (OH^{-} ions. For example, the equivalents contained in sulphuric acid (H_{2}SO_{4}) is calculated as follows:

(molecular weight of H_{2}SO_{4})/(moles of proton furnished)

= 98/2 = 49. Since each mole of H_{2}SO_{4} produces two protons.

(a) At complete neutralization, the number of equivalents of acid in the 12.5 ml volume is equal to the number of equivalents of base in the 20 ml volume.

normality, N = equivalents/liters.

So,N_{acid}V_{acid} = N_{base}V_{base} -------- (2)

N_{acid} in 50 ml (0.050 l) = number of equivalents in 0.050 l/0.050

= (mass of acid/gram equivalent weight)/0.050

= (0.490/49)/0.050 = 0.200 N.

So from equation (2), N_{base} = (N_{acid}V_{acid})/V_{base}

So, N_{base} = (0.200 x 12.5)/20 = 0.125 N.

Since molarity = number of mole/liters and there is 1 ionizable OH- in NaOH:

Normality = Molarity

So, concentration of the sodium hydroxide solution is 0.125 N or 0.125 M.

(b) The neutralization reaction between HCl and Al(OH)_{3} is:

Al(OH)_{3} + 3HCl --------> AlCl_{3} + 3H_{2}O -------(3)

At complete neutralization, the number of equivalents of Al(OH)_{3} equals the number of equivalents of HCl.

So, N_{HCl}V_{HCl} = N_{Al(OH)3}V_{Al(OH)3} -------- (4)

Where N is normality and V is volume.

Molarity of Al(OH)_{3} = (2.6/78)/0.100 = 0.33 M

Al(OH)_{3} contains 3 ionizable hydroxl (OH^{-}) ions

So, N_{Al(OH)3} = 3 x 0.33 = 0.99 N

Since HCl contains 1 ionizable ion, molarity of HCl = N_{HCl}

So, N_{HCl} = 80 x 10^{-3} N

So, V_{Al(OH)3} = (N_{HCl}V_{HCl})/N_{Al(OH)3}

= (80 x 10^{-3} N x 3 liters)/0.99 N = 0.240 liters = 240 ml

So, daily dose of medication is 240 ml.

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Single Variable Functions

Absolute Value Functions

Conics

Real Numbers

Vector Spaces

Equation Of The Ascent Path Of An Airplane

Calculating Capacity Of A Video Adapter Board Memory

Probability Density Functions

Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Advanced Calculus - Partial Derivatives

Advanced Calculus - General Charateristics Of Partial Differential Equations

Advanced Calculus - Jacobians

Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables

Advanced Calculus - Fourier Series

Advanced Calculus - Multiple Integrals

Production Schedule That Maximizes Profit Given Constraint Equation

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

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