A 50.0-g silver object and a 50.0-g gold object are both added to 75.5 mL of water contained in a graduated cylinder. What is the new water level, in milliliters, in the cylinder (see TABLE 2.8)? (2.7)

Verified step by step guidance

1. Identify the densities of silver and gold from TABLE 2.8. Let's assume the density of silver is ${\rho }_{\text{Ag}}$ and the density of gold is ${\rho }_{\text{Au}}$.
2. Calculate the volume of the silver object using the formula: $V_{\text{Ag}}=\frac{m_{\text{Ag}}}{{\rho }_{\text{Ag}}}$, where $m_{\text{Ag}}=50.0\text{ g}$.
3. Calculate the volume of the gold object using the formula: $V_{\text{Au}}=\frac{m_{\text{Au}}}{{\rho }_{\text{Au}}}$, where $m_{\text{Au}}=50.0\text{ g}$.
4. Add the volumes of the silver and gold objects to the initial water volume to find the new water level: $V_{\text{new}}=75.5\text{ mL}+V_{\text{Ag}}+V_{\text{Au}}$.
5. The result from the previous step gives the new water level in the graduated cylinder.

Key Concepts

Density

Density is defined as mass per unit volume and is a critical property of materials. It determines how much space an object occupies relative to its mass. In this scenario, the densities of silver and gold will influence how much water is displaced when these objects are submerged, which is essential for calculating the new water level.

Displacement of Water

The principle of water displacement states that when an object is submerged in a fluid, it pushes aside a volume of fluid equal to the volume of the object. This principle is fundamental in determining the new water level in the graduated cylinder after adding the silver and gold objects, as the total volume of the objects will directly affect the water level.

Volume Calculation

Volume calculation involves determining the space occupied by an object, which can be derived from its mass and density. For the silver and gold objects, knowing their masses allows us to calculate their respective volumes using the formula: Volume = Mass/Density. This calculation is necessary to find the total volume of water displaced and thus the new water level in the cylinder.