The molarity of sulfuric acid in a fully charged car battery is 5.2 m. when fully discharged the molarity is 4.8m. a 2.00ml sample of battery acid was titrated with 31.26ml of a.621 m sodium hydroxide solution. does the battery need to be recharged

This question requires utilization of  the equivalence point of a reaction, which is a point in the chemical reaction where the two solutions have been mixed in exactly the right proportions. This means that,

, where is the molarity of the acid sulfuric acid, the volume of acid, is the molarity of the base sodium hydroxide and is the volume of the base.

First we write a balanced equation,

.

The stochiometric ratio of is 1:2. Which means 1 mol react with 2 mol. Using the volume and molarity of  given we find the molarity of .

Using moles of we find the molarity

It is fully discharged so the battery needs to be recharged.

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