Respuesta :
The question requires us to calculate the volume of concentrated HNO3 solution (concentration = 16.0 mol/dm^3) to prepare 100 cm^3 of a 0.50 mol/dm^3 HNO3 solution.
We need to calculate the volume necessary from a concentrated solution to prepare a more dilluted solution. The number of moles of HNO3 in the solutions will not change, thus we can say:
[tex]n_1=n_2[/tex]where n is the number of moles of HNO3 and 1 and 2 refers to the initial solution and final solution, respectively.
The number of moles in a solution can be calculated as it follows:
[tex]C=\frac{n}{V}\to n=C\times V[/tex]where C is the concentration and V is the volume of the solution.
We can combine these two equations to have the following expression:
[tex]n_1=n_2\to C_1\times V_1=C_2\times V_2[/tex]With this expression, we can use the values given by the question to calculated the volume of the concentrated solution (V1) necessary to prepare a more dilluted solution:
[tex]\begin{gathered} C_1\times V_1=C_2\times V_2\to(16.0\frac{mol}{dm^3})\times V_1=(0.50\frac{mol}{dm^3})\times(100cm^3) \\ V_1=\frac{(0.50\text{ mol/dm}^3)\times(100cm^3)}{(16.0\text{ mol/dm}^3)}=3.12cm^3 \end{gathered}[/tex]Therefore, the volume necessary of concentrated HNO3 to prepare 100 cm^3 of 0.50 mol/dm^3 HNO3 solution is 3.12 cm^3.
