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Question: How many grams of oxalic acid dihydrate\({{(COOH)}_{2}}.x{{H}_{2}}O\), is needed to prepare \(525mL\...

How many grams of oxalic acid dihydrate(COOH)2.xH2O{{(COOH)}_{2}}.x{{H}_{2}}O, is needed to prepare 525mL525mL of a 0.570M0.570M solution?

Explanation

Solution

The molarity establishes a relationship between volumes of the solution with the number of moles of solute.
On the other hand, the number of moles of solute, establishes a relationship between the mass of the solute and the molar mass of the solute.

Complete solution:
First we need to calculate the number of moles of oxalic acid which is present in 525mL525mL of solution. We know that the number of moles of oxalic acid dihydrate would be a multiplication of the given volume and the molarity or the concentration of the same solution. So, we have,
525mL×10−3L×0.570molL−1525mL\times {{10}^{-3}}L\times 0.570mol{{L}^{-1}}
We convert the millilitre into the litre so as to convert it into the standard units, which also fits the definition of molarity. In other words, we convert the millilitre into litre because, molarity is the number of moles of solute present per litre of solution.
So, after solving the above equation we get 0.299moles0.299moles of oxalic dihydrate.
Now, we will use this value of the number of moles to determine the amount of oxalic acid, contained by it. So, we must first write down the values of the quantities which we have, for a better understanding.
We know that the number of moles of oxalic dihydrate is 0.299moles0.299moles, and the molar mass of oxalic dihydrate is 126.07gmol−1126.07gmo{{l}^{-1}}. So, the number of moles and the molar mass have a direct relation with the mass of a substance, as we know that the number of moles of a substance is the given mass, in this case unknown mass, of a substance present per molar mass of the same substance. So, we will use this to find the unknown mass of the substance, we get,
126.07gmol−1×0.299mol=mass126.07gmo{{l}^{-1}}\times 0.299 mol=mass
So the mass of the substance is the multiplication of the molar mass and the number of moles of the substance. So, we got 37.69g37.69g of oxalic acid dihydrate, which is the desired answer.

Note: The mass of oxalic acid dihydrate can be calculated by using the number of moles of oxalic acid present per certain volume of the solution, with the use of definition of molarity.
Then, we use the definition of number of moles to calculate the unknown mass of the oxalic acid.