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Question: What volume of \(75\% \) alcohol by mass (\(d\)=\(0.8g/c{m^3}\)) must be used to prepare \(150cc\)of...

What volume of 75%75\% alcohol by mass (dd=0.8g/cm30.8g/c{m^3}) must be used to prepare 150cc150ccof 30%30\% alcohol by mass (dd=0.9g/cm30.9g/c{m^3})?
A. 44.44mL44.44mL
B. 56.25mL56.25mL
C. 67.5mL67.5mL
D. 33.56mL33.56mL

Explanation

Solution

Volume percentage is the ratio of Volume of the component of the solution and the total mass of the solution which is multiplied by 100. Volume is defined as the amount of three-dimensional space or area covered by a shut surface.

Complete Step by step solution:
Firstly we will assume that VmLVmLamount of alcohol is required in the solution.
Now as given in question the value of mass and density we will solve to get required volume.
∵ Mass of alcohol is same in both solutions.
Hence the following equation will be formed,
100×0.8×V75\dfrac{{100 \times 0.8 \times V}}{{75}}=100×0.9×150V30\dfrac{{100 \times 0.9 \times 150V}}{{30}}
On solving the above equation we will get the volume of alcohol used in it.
=67.5mL67.5mL.

So, the correct answer is C.

Additional information:
Three dimensional are the numerical shapes which are likewise doled or copy out volumes. Volumes of some common and basic shapes, for instance, standard shapes, straight-edged shapes, and round shapes can be easily determined by using so many math recipes or methods. Volumes of confounded shapes need to be determined with or by basic math methods, if that equation exists for the shape's limit. One-dimensional figures means only one direction or simple shapes, (for example, lines) and two-dimensional shapes, (for example, squares) are allocated with zero volume in the three-dimensional space as they are negligible in the space of three dimensional areas.
The volume of a strong (either they are of consistently or sporadically molded no matter) can be calculated by liquid uprooting. Relocation or changing in location of fluid can be used to utilize the decided volume of a gas. The joined volume of two substances is typically more projecting compared with the volume of only one of the substances. Nonetheless, if now and again one substance breaks down in the other substances and in these such cases the joined volume isn't added to the substance.

Note: In the International System of Units, the standard unit of volume is the cubic meter (m3{m^3}). The metric system also includes the liter (LL) as a unit of volume, where one liter is the volume of a 1010-centimeter cube.