Respuesta :
Answer:
To determine the density of the mixture after Phionah mixed 400 cm³ of salt solution with water, you need to know the densities of both the salt solution and water.
Let's assume the density of water is \( \rho_{\text{water}} = 1 \, \text{g/cm}^3 \).
Given that Phionah mixed 400 cm³ of salt solution with a density of \( \rho_{\text{salt}} = 1.6 \, \text{g/cm}^3 \), you can calculate the total mass of the mixture and then find the overall density.
The mass of the salt solution is given by the formula:
\[ \text{Mass}_{\text{salt}} = \text{Volume}_{\text{salt}} \times \text{Density}_{\text{salt}} \]
\[ \text{Mass}_{\text{salt}} = 400 \, \text{cm}^3 \times 1.6 \, \text{g/cm}^3 \]
\[ \text{Mass}_{\text{salt}} = 640 \, \text{g} \]
The mass of water is given by:
\[ \text{Mass}_{\text{water}} = \text{Volume}_{\text{water}} \times \text{Density}_{\text{water}} \]
Since water has a density of \( \rho_{\text{water}} = 1 \, \text{g/cm}^3 \), and the volume of water is the remaining volume after adding the salt solution (considering the total volume is 400 cm³), we can calculate it as:
\[ \text{Volume}_{\text{water}} = \text{Total volume} - \text{Volume}_{\text{salt}} \]
\[ \text{Volume}_{\text{water}} = 400 \, \text{cm}^3 - 400 \, \text{cm}^3 = 0 \, \text{cm}^3 \]
Therefore, the mass of water is 0 g.
Now, the total mass of the mixture is the sum of the masses of the salt solution and water:
\[ \text{Total mass} = \text{Mass}_{\text{salt}} + \text{Mass}_{\text{water}} \]
\[ \text{Total mass} = 640 \, \text{g} + 0 \, \text{g} = 640 \, \text{g} \]
The total volume of the mixture is 400 cm³.
Finally, the density of the mixture is given by the formula:
\[ \text{Density}_{\text{mixture}} = \frac{\text{Total mass}}{\text{Total volume}} \]
\[ \text{Density}_{\text{mixture}} = \frac{640 \, \text{g}}{400 \, \text{cm}^3} \]
\[ \text{Density}_{\text{mixture}} = 1.6 \, \text{g/cm}^3 \]
Therefore, the density of the mixture is \( 1.6 \, \text{g/cm}^3 \).
