# Density of Solution and mass percent

There are two numericals,

1. Density of Methanol is 0.793 kg/l. Find molarity. ANSWER is : Desity/ Molar mass = Molarity (UNDERSTANDABLE)

In other numerical
2. Concentration of H2SO4 is 98% by mass having density of 1.84gm/ml. Calculate Molarity.
here they used another formula.

now my question is, How second question is different from First ? why didnt they took density and devided it by Molar mass to get molarity?
What I am missing?

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## Answers and Replies

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Dr. Courtney
Gold Member
The density of your H2SO4 looks wrong to me.

Sorry ! Corrected. It was missing decimal.

RUber
Homework Helper
I imagine the difference is in the concentration. If H2SO4 is 98% of the concentration by mass, is the 1.84gm/ml the density of H2SO4 or the density of the concentration?
Perhaps if you posted the formula you are looking at, it would make clear what the example is trying to show.

Chestermiller
Mentor
Take as a basis 1 liter of solution. What is the mass of this 1 liter of solution? If the mass fraction of sulfuric acid is 0.98, what is the mass of sulfuric acid in the 1 liter of solution? How many moles is that?

Chet

Formula is MOLARITY = (%age * density *10)/ Density

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What is the mass of this 1 liter of solution? If the mass fraction of sulfuric acid is 0.98, what is the mass of sulfuric acid in the 1 liter of solution? How many moles is that?
Sorry I didnt get what you are implying.
Here is another way to Present my Doubt. We say that Molarity of Pure water is 55.5 ( which we calculate by using Density as 1)
Now By giving mass percentage, What extra information is given ?

SECOND: what is difference between STRENGTH of soln. and DENSITY of solution.

Bystander
Homework Helper
Gold Member
Giving you what?

Molarity

Well it is simple derivation, By considering mass of solution = 100gm and H2SO4 = 98gm
then they converted Mass of solution into VOLUME. and converted mass of H2SO4 into moles.
Once you have both of them, you can get molarity.

NOW my confusion is ..... Why didnt they simply converted DENSITY ( gm/ml) Into Molarity ( MOLES/ ml)
what I am missing?

Bystander
Homework Helper
Gold Member
Time to back up a couple steps; what is the definition of molarity?

Moles in Litre Solution

Bystander
Homework Helper
Gold Member
... and, if the density of 98% sulfuric acid is 1.84 g/cm3, one liter contains how many grams?

I think I got it ?
If I only consider Density : 1 litres contain 1840 gm ,
Now this 1840gm will be of weight of (Sulphuric acid + water) ?

Bystander
Homework Helper
Gold Member
Now this 1840gm will be of weight of (Sulphuric acid + water) ?
Yes. How much sulfuric acid?

Alright ...

SO 98gm H2SO4 in 100gm solution.
100 gm solution = 54.3 ml.

Weight of Sulphuric acid is = 98/54.3 * 1000 = 1804.8 gm

Bystander
Homework Helper
Gold Member
Correct. That will be how many moles?

18.4 moles

Thanks.

Chestermiller
Mentor
This would all have been much simpler if you had chosen as a basis of the calculation 1 liter of solution rather than 100 gm of solution (as I suggested in post #5).
mass of 1 liter of solution = 1840 gm
mass of H2SO4 = (0.98)(1840)=1804.8 gm
moles of H2SO4 = 18.4
moles H2SO4 per liter of solution = 18.4

Chet