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Question: The density of a \(60.00\% \) (m/m) ethanol, \({C_2}{H_5}OH\) solution is \(0.8937gm/ml\) what is th...

The density of a 60.00%60.00\% (m/m) ethanol, C2H5OH{C_2}{H_5}OH solution is 0.8937gm/ml0.8937gm/ml what is the molarity of solution? ( Molar mass = 46.07g/mole{\text{Molar mass = 46}}{\text{.07g/mole}})

Explanation

Solution

Weight percentage and molar concentration or molarity are the two terms related to the concentration in chemistry. The ratio of weight of solute to the weight of solution is known as the weight percentage and the ratio of moles of solute to the volume of solution is known as the molarity.

Complete step by step answer:
The number of moles present in one liter of solution is known as the molarity. Basically it is the concentration term used to define concentration of solutes present in the solvent. The molar concentration or molarity is represented as ’M’{\text{'M'}} .
The formula for molar concentration is as follows:
Molarity = Moles of soluteVolume of solution(L) {\text{Molarity = }}\dfrac{{{\text{Moles of solute}}}}{{{\text{Volume of solution}}(L)}}{\text{ }}
The weight percentage or %w/w\% w/w represents the weight ratio of solute and the solution.
The formula representation for the weight percentage is as follows:
%w/w=mass of solutemass of solution×100\% w/w = \dfrac{{{\text{mass of solute}}}}{{{\text{mass of solution}}}} \times 100
In this problem the data provided to us is as follows:
Density of solution= 0.8937g/ml0.8937g/ml
Weight percentage of ethanol=60.00%60.00\%
Molar mass of ethanol=46.07gm/mole46.07gm/mole
And we know very well that the unique relation between weight percentage and molarity is as follows:
M=%w/w×d×10Molecular weight{\text{M}} = \dfrac{{{\% w/w \times d \times 10}}}{{{\text{Molecular weight}}}}
So by putting the provided values in this formula we will get our required molarity.
Therefore, M=60×0.8937×1046.07{\text{M}} = \dfrac{{{60 \times 0}}{.8937 \times 10}}{{46.07}}
M = 11.63 mol L - 1{\text{M = 11}}{\text{.63 mol }}{{\text{L}}^{{\text{ - 1}}}}

Additional information: In chemistry, the amount of substance defined in a definite space is known as concentration. The formula for concentration varies according to our requirements, if we want to calculate concentration in terms of weight or in terms of moles, it depends upon us and our compatibility.

Note: We have different formulas related to the concentration such as for molarity, for weight percentage, for molality and many more but the standard formula for the calculation of concentration is related to mass and volume of the solution. The formula is C = m/v{\text{C = m/v}} where C is the concentration, m is mass and v is volume.