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InterviewSolution
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Converting mass percent to molarity: the density of a 24.5 mass % solution of sulphuric acid `(H_(2)SO_(4))` in water is `1.176 g mL^(-1)` at `25.0^(@)C`. What is the molarity of the solution? Stregy: Use mass % to calculate number of moles of solute and use density of solution to calculate volume of solution. Describing a solution as 24.5 mass % `H_(2)SO_(4)` in `H_(2)O` means that every 100.0 g of solution contains 24.5 g of `H_(2)SO_(4)` and 75.5 g of `H_(2)O`. Since we want to calculate the concentration in molarity, we first need to find the number of moles of `H_(2)SO_(4)` dissolved in a specific mass of solution. Next we use density as a conversion factor to find the volume of that solution and then calculate molarity by dividing the number of moles of `H_(2)SO_(4)` by the volume of solution. |
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Answer» Consider `100.0 g` of solution. Therefore, mass of `H_(2)SO_(4)` is `24.5 g`. First, convert the mass of `H_(2)SO_(4)` into moles. `n_(H_(2)SO_(4))=(Mass H_(2)SO_(4))/(Molar mass H_(2)SO_(4))` `=(24.5 g H_(2)SO_(4))/(98.0 g H_(2)SO_(4)//mol H_(2)SO_(4))` `=0.25 mol H_(2)SO_(4)` Next, we find the volume of `100.0 g` of solution using sensity as the conversion factor: Volume of solution`=((1216g)/(1000mL))/((100.0" g soln")/(1.176"g soln"//mL))` `=85mL` `=85 mL` Finally, calculate the molarity of solution using Eqution `2.14`. Molarity`=n_(H_(2)SO_(4))/V_(mL)xx(1000 mL)/L` `=(0.25 mol H_(2)SO_(4))/(85 mL soln)xx(1000 mL)/L` `=2.94 M` Thus, the molarity of the `24.5` mass `%` of sulphuric acid solution is `2.94 M`. Short cut method: We can also convert mass percent into molarity by using the following formula: `M=("(mass%)(specific gravity or density of soln)(10)")/(("molar mass of solute"))` `=((24.5)(1.175)(10))/98` `=2.94 mol L^(-1)` |
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