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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