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# change of base formula

From Wikipedia

Acid-base titration

An acid-basetitrationis the determination of the concentration of an acid or base by exactly neutralizing the acid/base with an acid or base of known concentration. This allows forquantitative analysis of the concentration of an unknown acid or basesolution. It makes use of the neutralization reaction that occurs between acids and bases and the knowledge of how acids and bases will react if their formulas are known.

Acid-base titrations can also be used to find percent purity of chemicals.

## Alkalimetry and acidimetry

Alkalimetry, sometimes spelled alkimetry, is the specialized analytic use of acid-base titration to determine the concentration of a basic (synonymous to alkaline) substance. Acidimetry, sometimes spelled acidometry, is the same concept of specialized analytic acid-base titration, but for an acidic substance.

## Equipment

The key equipment used in a titration are:

## Method

Before starting the titration a suitable pH indicator must be chosen. The equivalence point of the reaction, the point at which equivalent amounts of the reactants have reacted, will have a pH dependent on the relative strengths of the acid and base used. The pH of the equivalence point can be estimated using the following rules:

• A strong acid will react with a strong base to form a neutral (pH=7) solution.
• A strong acid will react with a weak base to form an acidic (pH<7) solution.
• A weak acid will react with a strong base to form a basic (pH>7) solution.

When a weak acid reacts with a weak base, the equivalence point solution will be basic if the base is stronger and acidic if the acid is stronger. If both are of equal strength, then the equivalence pH will be neutral. However, weak acids are not often titrated against weak bases because the colour change shown with the indicator is often quick, and therefore very difficult for the observer to see the change of colour.

The point at which the indicator changes colour is called the end point. A suitable indicator should be chosen, preferably one that will experience a change in colour (an end point) close to the equivalence point of the reaction.

First, the burette should be rinsed with the standard solution, the pipette with the unknown solution, and the conical flask with distilled water.

Secondly, a known volume of the unknown concentration solution should be taken with the pipette and placed into the conical flask, along with a small amount of the indicator chosen. The burette should always be filled to the top of its scale with the known solution for ease of reading.

The known solution should then be allowed out of the burette, into the conical flask. At this stage we want a rough estimate of the amount of this solution it took to neutralize the unknown solution. The solution should be let out of the burette until the indicator changes colour and the value on the burette should be recorded. This is the first (or rough) titre and should be discluded from any calculations.

Three more titrations should be performed, this time more accurately, taking into account roughly where the end point will occur. The readings on the burette at the end point should be recorded, and averaged to give a final result. The end point is reached when the indicator just changes colour permanently. This is best achieved by washing a hanging drop from the tip of the burette into the flask right at the end of the titration to achieve a drop that is smaller in volume than what can usually be achieved by just dripping solution off the burette.

Acid-base titration is performed with a phenolphthalein indicator, when it is a strong acid - strong base titration, a bromthymol blue indicator in weak acid - weak base reactions, and a methyl orange indicator for strong acid - weak base reactions. If the base is off the scale, i.e. a pH of >13.5, and the acid has a pH >5.5, then an Alizarine yellow indicator may be used. On the other hand, if the acid is off the scale, i.e. a pH of <0.5, and the base has a pH <8.5, then a Thymol Blue indicator may be used.

## Titration of weak acid

When titrating a weak acid with a strong base, the pH before the equivalence point can be calculated by the following formula:

where:

• pKa is the negative log of the acid dissociation constant of the weak acid.
• [OH-]added is the concentration of added strong base in the final solution (not in original standard solution)
• [HA]total is the summed concentration of both the weak acid and its conjugate base in the final solution.

Thus, at an addition of strong base that is half the amount of weak acid in the solution ([OH-]added = 0.5[HA]total), pH becomes equal to pKa.

The more general formula that describes the titration of a weak acid with a strong base is given below

\phi = \frac{ C_b V_b }{C_a V_a} = \frac{\alpha_{A^-} - \frac{[H^+] - [OH^-]}{C_a}}{1 + \frac{[H^+] - [OH^-]}{C_b}}

\alpha_{A^-} = \frac {K_a}{[H^+] + K_a}

• \phi = fraction of completion of the titration (\phi < 1 is before the equivalence point, \phi = 1 is the equivalence point, and \phi > 1 is after the equivalence point)
• C_a, C_b = the concentrations of the acid and base respectively
• V_a, V_b = the volumes of the acid and base respectively
• \alpha_{A^-} = the fraction of the weak acid that is ionized
• K_{a} = the dissociation constant for the acid
• [H^+], [OH^-] = concentrations of the H^+ and OH^- ions respectively

Question:This log problem says to use the "Change of Base Formula" to rewrite this common logarithm? 1. log2 10 I'm not sure what it means. Also, problem number 2 says "solve the log, and round to the nearest thousandth" 2. ln 2 plus ln x = 1 Does anyone understand these?

Answers:let log2_10 =x then 2^x =10 ln2 + lnx =1 ln2x =1 e^ln2x = e^1 =e 2x = e x=e/2 use calculator to find the exact value! I do not have one here.

Question:The number I need to change is 361. This is for my math and I really dont get this. I need to know the formula, or at least how you get the answer because my teacher requires us to show our work.

Answers:Divide by 8 repeatedly, rounding down each time, until you reach 0. Then list the remainders in reverse order. Example: Convert 12345 from base 10 to base 8. 12345 / 8 = 1543 r. 1 1543 / 8 = 192 r. 7 192 / 8 = 24 r. 0 24 / 8 = 3 r. 0 3 / 8 = 0 r. 3 The remainders (in reverse order) are 3,0,0,7,1. So 12345 (base 10) = 30071 (base 8)

Question:For example if the number in base 10 is 41, how could i change it to base 2? Please tell me how you did it? Please give me the formula?