Question

1. alicias cheapskate boyfriend gave her a ring he claims is 24 carat gold. alicia is skeptical. after chemistry class the next day she measures the mass of the ring, finds the volume of the ring by water displacement, and then calculates the density of the ring. should she treasure the ring as his first truly generous gift to her, or throw it at him the next time he walks by? defend your answer.

data:
mass: 15.28 g
final volume= 43.7 ml
initial volume= 42.2 ml
volume of ring=
density =?

1. a student filled a graduated cylinder with water and read the meniscus at 25.8 ml. the student then dropped a solid material into the graduated cylinder and the water level rose to 35.9 ml. if the solid material had a density of 2.99 g/ml, determine the mass of the solid object. work wisely.

Explanation:

Step1: Calculate volume of ring

The volume of the ring is found by the difference in water - levels in the displacement method. So, $V = 43.7\mathrm{mL}-42.2\mathrm{mL}=1.5\mathrm{mL}$

Step2: Calculate density of ring

The density formula is $
ho=\frac{m}{V}$. Given $m = 15.28\mathrm{g}$ and $V = 1.5\mathrm{mL}$, then $
ho=\frac{15.28\mathrm{g}}{1.5\mathrm{mL}}\approx10.19\mathrm{g/mL}$
The density of 24 - carat gold is approximately $19.3\mathrm{g/mL}$. Since the calculated density of the ring is much lower than that of 24 - carat gold, it is likely not 24 - carat gold.

Step3: Solve for mass of solid in second problem

First, find the volume of the solid. The volume of the solid is the change in water - level in the graduated cylinder. So, $V_{solid}=35.9\mathrm{mL}-25.8\mathrm{mL}=10.1\mathrm{mL}$
Using the density formula $
ho=\frac{m}{V}$, we can solve for $m$. Rearranging gives $m=
ho V$. Given $
ho = 2.99\mathrm{g/mL}$ and $V = 10.1\mathrm{mL}$, then $m=2.99\mathrm{g/mL}\times10.1\mathrm{mL}\approx30.2\mathrm{g}$

Answer:

The volume of the ring is $1.5\mathrm{mL}$, the density of the ring is approximately $10.19\mathrm{g/mL}$ (it is likely not 24 - carat gold), and the mass of the solid object in the second problem is approximately $30.2\mathrm{g}$