In an acid-base titration, a base or acid is gradually added to the other until

Question

In an acid-base titration, a base or acid is gradually added to the other until they have completely neutralized each other.Because acids and bases are usually colorless(as are the water and salt produced in the neutralization reaction),pH is measured to monitor the reaction.Suppose tha equivalence point is reached after approximately 100mL of NaOH solution have been added( enough to react with all the acetic acid present) but that replicates are equally likely to indicate from 95 to 104 mL to the nearest mL.Assume that volumes are measured to the nearest ML and describe the sample space.

a)What is the probability that equivalence is indicated at 100 mL ?

b) What is the probability that equivalence is indicated at less than 100 mL ?

c) What is the probability that equivalence is indicated between 98 and 102 mL (inclusive) ?

Explanation / Answer

If replicates are equally likely to measure any volume between 95 and 104 ml, your sample space is any real number in the interval [95, 104] Since measuring is never going to give you a very precise measure of the volume, you could also assume that your sample space is a list of discrete possible measures (say, 95ml , 95.1ml, 95.2ml,.....104ml) In any case, since the measures are equally likely, your variable (X = volume of NaOH poured to achieve neutralization) is uniformly distributed in the given sample space. a) The question seems to suggest you cannot reach a precision better than 1ml. In that case, X is uniformly distributed in {95, 96, 97, 98, 99, 100, 101, 102, 103, 104}. That is 10 possible measures. The probability of any one of those is 1/10 because the variable is uniformly distributed. For any event i in the sample space, P(Xi) = 0.1 P(X = 100) = 0.1 b) P(X

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