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Solutions: Percentage by mass (1931)
Sábado 10 de noviembre de 2012, por
Make a solution by mixing 22 g of sugar and 240 mL of milk. Determine the percentage by mass of this solution. How much sugar is needed to prepare 500 g of solution with the same concentration?
Average density of milk is 
.
The mass of milk used for the mixture is:
![240\ \cancel{mL}\cdot \frac{1.03\ g}{1\ \cancel{mL}} = \color[RGB]{0,112,192}{\bf 247.2\ g}](local/cache-vignettes/L248xH47/1c73770d1fdf774e1bbc902ec655d4ad-bde90.png?1732956019 "240\ \cancel{mL}\cdot \frac{1.03\ g}{1\ \cancel{mL}} = \color[RGB]{0,112,192}{\bf 247.2\ g}"){kind=small}
The total mass of the solution is:
![m_T = m_S + m_d = (22 + 247.2)\ g\ \to\ m_D = \color[RGB]{0,112,192}{\bf 269.2\ g}](local/cache-vignettes/L482xH23/fd21c5fc2aaa88031f7651d4930c3e9f-e2d61.png?1732956019 "m_T = m_S + m_d = (22 + 247.2)\ g\ \to\ m_D = \color[RGB]{0,112,192}{\bf 269.2\ g}"){kind=small}
The mass percentage is:
![\%(m) = \frac{m_S}{m_T}\cdot 100 = \frac{22\ \cancel{g}}{269.2\ \cancel{g}}\cdot 100 = \fbox{\color[RGB]{192,0,0}{\bf 8.17\ \%}}](local/cache-vignettes/L416xH51/38cb9992a9391a5d6a27803de6e81f53-08f0a.png?1732956019 "\%(m) = \frac{m_S}{m_T}\cdot 100 = \frac{22\ \cancel{g}}{269.2\ \cancel{g}}\cdot 100 = \fbox{\color[RGB]{192,0,0}{\bf 8.17\ \%}}")
The obtained result indicates that you need 8.17 g of sugar to prepare 100 g of solution:
![500\ \cancel{g\ D}\cdot \frac{8.17\ g\ S}{100\ \cancel{g\ D}} = \fbox{\color[RGB]{192,0,0}{\bf 40.9\ g\ S}}](local/cache-vignettes/L297xH52/e25d3d805fa0d6cf5030bbc04c5e644e-1bc85.png?1732956019 "500\ \cancel{g\ D}\cdot \frac{8.17\ g\ S}{100\ \cancel{g\ D}} = \fbox{\color[RGB]{192,0,0}{\bf 40.9\ g\ S}}")