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Question: How many grams of solid sodium hydroxide are required to make \(175mL\) of a \(0.5100M\) \(NaOH\) so...

How many grams of solid sodium hydroxide are required to make 175mL175mL of a 0.5100M0.5100M NaOHNaOH solution?

Explanation

Solution

The amount of a substance in terms of grams, in a fixed volume of solution, can be calculated by using its molarity. At first we would calculate the number of moles of that substance in one mole which is already given as the molarity, then we will find out the number of moles in that fixed volume of the solution.
After that we will calculate the mass of that substance by using the number of moles and molecular mass, as per the definition of the number of moles, which is, mass of the substance present per molar mass of that substance.

Complete answer:
Molarity of a substance can be defined as the number of moles of that substance present per litre of the solution of that substance. It is a measure to express the concentration of the solute present in the solution.
It is given to us that the molarity of sodium hydroxide is 0.5100M0.5100M, which tells us that 0.5100moles0.5100moles of sodium hydroxide is present in one litre of the solution. So, in order to calculate the number of moles present in 175mL175mL of the solution, we will just multiply the value, we get,
0.17500Lsoln×0.5100molNaOH1Lsoln=0.08925molNaOH0.17500L{ }soln\times \dfrac{0.5100{ }mol{ NaOH}}{1L{ }soln}=0.08925{ }mol{ }NaOH
So, now we know that the number of moles of sodium hydroxide on 175mL175mL solution is 0.089250.08925 moles. Now, we will calculate the mass of sodium hydroxide in this number of moles.
We know that the mass of one mole of sodium hydroxide is, 23+16+1=40g23+16+1=40g, as the mass of one sodium atom, one oxygen atom and one hydrogen atom is 23,16,123,16,1 respectively.
So, in order to calculate the mass of sodium hydroxide in 0.089250.08925 moles of it, we would multiply the values, and we get,
0.08925molNaOH×40.00gNaOH1molNaOH=3.570gNaOH0.08925molNaOH\times \dfrac{40.00gNaOH}{1molNaOH}=3.570gNaOH
So, we got 3.570g3.570g of sodium hydroxide, which is the required answer.

Note: At first we found out the number of moles of sodium hydroxide present in 175mL175mL of the solution, by using the definition of the molarity.
Then we determined the mass of the sodium hydroxide present in that many moles of the sodium hydroxide, by using the definition of number of moles, which is mass of a substance present per molecular mass.