What would be the mass by volume percentage of a solution which is 20% mass by mass density of the solution is 1.02 g mL 1?

The solution has 15% acid, means 15g/100ml.The density is of solution is 1.02g/ml.Mass of solution having 15g of acid= density × volume= 1.02 g/ml × 100 ml=102 gSo, mass of water = mass of solution-mass of acid=102 – 15=87 g Acid present with 87 g of water is 15 g.So, acid present with 100 g of water.=100 X 87/15 = 17.24/100 g of waterThe density of water is 1g/ml.So, the concentration will be 17.24/100 ml of water.

So, the mass by volume percentage is 17.24 %.

Concept:

Mass by volume percentage = (mass of solute/volume of solution) x 100.

• It measures solute mass or weight in grams (e.g., in grams) vs. solution volume (e.g., in mL).
• An example would be a 0.9 percent (w/v) NaCl solution containing 0.9 g of NaCl per 100 mL of solution in medical saline solutions.
• The mass/volume percentage is used to express a solution's concentration when the solute mass and solution volume are given.
• The mass percentage is used when the mass of a solute and the mass of a solution express the concentration of a solution.
• Mass by mass percentage = (mass of solute/mass of solution) x 100

Calculation:

Given,

Mass by mass % = 20% = (mass of solute/mass of solution) ×  100

Density of the solution = 1.02 g mL-1 = (mass of solution/ volume of solution ) × 100

We know that,

\(Mass\;by\;volume\;\% = \frac{{mass\;of\;solute}}{{volume\;of\;solution}} \times 100\)

we have to find the mass of solute =?

Volume of the solution =?

Also,

\(Mass\;by\;mass\;\% = 20\;\% = \frac{{mass\;of\;solute}}{{mass\;of\;solution}} \times 100\)

\( \Rightarrow Mass\;of\;Solute = \frac{{20}}{{100}} \times mass\;of\;solution = 0.2 \times mass\;of\;solution\).................(Eq - 1)

Also,

\(Density\;of\;Solution\;\left( {1.02} \right) = \frac{{mass\;of\;solution}}{{Volume\;of\;solution}}\)

\(\Rightarrow Volume\;of\;Solution = \frac{{mass\;of\;solution}}{{Density\;of\;Solution\;\left( {1.02} \right)}}\) .................. (Eq - 2)

Putting the values (Eq- 1) and (Eq -2) in

\(Mass\;by\;volume\;\% = \frac{{mass\;of\;solute}}{{volume\;of\;solution}} \times 100\)

\( \Rightarrow Mass\;by\;volume\;\% = \frac{{\left( {0.2 \times mass\;of\;solution} \right)}}{{\left( {\frac{{mass\;of\;solution}}{{1.02}}} \right)}} \times 100 = 0.2 \times 1.02 \times 100 = 20.4\;\% \)

Hence the correct option is 20.4 %

Calculate mass/volume percentage of 20 % solution by mass of sulphuric acid

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