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 the ring

The volume of the ring is found by the difference between the final and initial volumes of water in the displacement method. So, $V = V_{final}-V_{initial}$. Given $V_{final}=43.7\ mL$ and $V_{initial}=42.2\ mL$, then $V=43.7 - 42.2=1.5\ mL$.

Step2: Calculate density of the ring

The density formula is $
ho=\frac{m}{V}$, where $m = 15.28\ g$ and $V = 1.5\ mL$. So, $
ho=\frac{15.28}{1.5}\approx10.19\ g/mL$.
The density of 24 - carat gold is 19.32 g/mL. Since the calculated density of the ring ($10.19\ g/mL$) is much lower than the density of 24 - carat gold, she should throw it at him.

For the second problem:

Step1: Calculate volume of the solid

The volume of the solid is the difference in water levels in the graduated - cylinder. So, $V = 35.9 - 25.8=10.1\ mL$.

Step2: Calculate mass of the solid

Using the density formula $
ho=\frac{m}{V}$, we can re - arrange it to $m=
ho\times V$. Given $
ho = 2.99\ g/mL$ and $V = 10.1\ mL$, then $m=2.99\times10.1 = 30.199\ g\approx30.2\ g$.

Answer:

For the ring problem:
Volume of ring: 1.5 mL
Density of ring: approximately 10.19 g/mL. She should throw it at him as the density is much lower than that of 24 - carat gold.
For the solid problem: Mass of the solid object is approximately 30.2 g.