A 25.5 g sample of a metal was placed into water in a gradu-ated cylinder. The metal sank to the bottom, and the water level rose from 15.7 mL to 25.3 mL. What is the identity of the metal? (LO 1.9) (a) Tin (density = 7.31 g/cm3) (b) Lead (density = 11.34 g/cm3) (c) Silver (density = 10.49 g/cm3) (d) Aluminum (density = 2.64 g/cm3)

Verified step by step guidance

1. First, we need to calculate the volume of the metal. We can do this by subtracting the initial volume of the water in the graduated cylinder from the final volume after the metal was added. In this case, the volume of the metal is 25.3 mL - 15.7 mL.
2. Next, we need to convert the volume of the metal from milliliters (mL) to cubic centimeters (cm^3) because the densities of the metals are given in g/cm^3. Remember that 1 mL is equivalent to 1 cm^3.
3. Now, we can calculate the density of the metal. Density is defined as mass divided by volume. In this case, the mass of the metal is 25.5 g and the volume is the value we calculated in the previous step.
4. Once we have the density of the metal, we can compare it to the densities of the metals given in the problem. The metal whose density is closest to the calculated density is likely to be the identity of the metal.
5. Remember that the densities given in the problem are average values. The actual density of a sample can vary slightly due to impurities or variations in temperature and pressure. Therefore, the metal with the density closest to the calculated value is the most probable identity of the metal, but it is not a definitive identification.

Key Concepts

Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³). It is a crucial property of materials that helps identify substances based on their physical characteristics. In this problem, the density of the metal can be calculated using the mass of the metal and the volume of water displaced, which corresponds to the volume of the metal.

Displacement Method

The displacement method involves measuring the volume of liquid displaced by an object when it is submerged. This technique is used to determine the volume of irregularly shaped objects, such as the metal in this question. The change in water level in the graduated cylinder indicates the volume of the metal, which is essential for calculating its density.

Identifying Metals by Density

Different metals have characteristic densities that can be used for identification. By calculating the density of the metal sample from its mass and the volume of water displaced, one can compare the calculated density to known densities of various metals. This comparison allows for the identification of the metal in question based on the closest match to its density.