Given:
The volume of alcohol, V_a=55 mL
The density of the alcohol, ρ_a=0.75 g/mL
The mass of the water in the mixture, M_w=25 g
The density of water, ρ_w=1.00 g/mL
To find:
The density of the mixture.
Explanation:
The mass of the alcohol in the mixture is given by,
[tex]\begin{gathered} M_a=V_a\rho_a \\ =55\times0.75 \\ =41.25\text{ g} \end{gathered}[/tex]
The volume of the water in the mixture,
[tex]V_w=\frac{m_w}{\rho_w}[/tex]
On substituting the known values,
[tex]\begin{gathered} V_w=\frac{25}{1.00} \\ =25\text{ mL} \end{gathered}[/tex]
Thus the density of the mixture is given by,
[tex]\begin{gathered} \rho_=\frac{total\text{ }mass}{total\text{ }volume} \\ =\frac{m_a+m_w}{V_a+V_w} \end{gathered}[/tex]
On substituting the known values,
[tex]\begin{gathered} \rho=\frac{41.25+25}{55+25} \\ =0.83\text{ g/mL} \end{gathered}[/tex]
Final answer:
Thus the density of the mixture is 0.83 g/mL
