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Question: What is the molarity of \({H_2}S{O_4}\) solution that has a density of \(1.84g/cc\) at \({35^0}C\) a...

What is the molarity of H2SO4{H_2}S{O_4} solution that has a density of 1.84g/cc1.84g/cc at 350C{35^0}C and contains 98%98\% by weight?
A . 4.18M4.18M
B . 8.14M8.14M
C . 18.4M18.4M
D . 18M18M

Explanation

Solution

Hint :In the mole concept we have studied about the molarity and we have studied that molar concentration of substance is also known as molarity. It is defined as the ratio of moles of substance to volume of solution in litre.

Complete answer:

Mole is defined as weight in grams divided by the molecular weight of the substance. So we will find out the molarity by the formula; M=Number of moles of solute /volume of the solution in litre.
As it is given in the problem that H2SO4{H_2}S{O_4} is 98%98\% by weight that means that 100g100g solution contains 98g98g H2SO4{H_2}S{O_4} by mass.
Density of solution of sulphuric acid is given that is 1.84g/cc1.84g/cc; Density=massVolumeDensity = \dfrac{{mass}}{{Volume}} Volume=massDensity \Rightarrow Volume = \dfrac{{mass}}{{Density}}
Volume=1001.84×1000L\Rightarrow Volume = \dfrac{{100}}{{1.84 \times 1000}}L
Volume=0.0543\Rightarrow Volume = 0.0543 Litre
Molecular weight of sulphuric acid (H2SO4{H_2}S{O_4}) = 2×atomic weight of hydrogen atomic weight of sulphur +4×atomic weight of oxygen
Molecular weight of sulphuric acid (H2SO4{H_2}S{O_4}) =2×1+32+4×16 = 2 \times 1 + 32 + 4 \times 16
=98= 98
- Now here weight of sulphuric acid in gram is 98g98g and molecular weight of sulphuric acid is 98g/mol98g/mol
- So first calculate the number of moles before calculating molarity. Number of moles of H2SO4{H_2}S{O_4}=Weight in gram of H2SO4{H_2}S{O_4}/ molecular weight of H2SO4{H_2}S{O_4}
=98/98= 98/98 =1 = 1
- Hence the molarity of H2SO4{H_2}S{O_4}=Number of moles /Volume in litre =10.0543=\dfrac{1}{{0.0543}}
=18.4M= 18.4M
So the correct option is (c) that is 18.4M18.4M.

Note : In mole problems we should always remember some important relation .Here in this problem we have used some relations to solve the problem as we have found the mass with the help of given density and then put the value of mass in the formula to find the number of moles. Once the number of moles is determined we calculate molarity of sulphuric acid easily with the help of molarity formula.