Question

a graduated cylinder is filled with 100.0 ml of water. the cylinder is placed on a mass balance and tared (zeroed). in three different studies, samples of solid are added to the cylinder. the mass of solid and the new volume reading are shown. tap the fields to rank the density values of sample a sample b sample c

Explanation:

Step1: Find solid volumes

Subtract initial water volume from final volumes.

Step2: Calculate densities

Apply $
ho=\frac{m}{V}$ formula for each sample.

Step3: Rank densities

Compare calculated density values.

Answer:

We need the volume readings of the graduated - cylinder with the solids added to calculate the density. Since the initial volume of water is 100.0 mL, the volume of the solid is the final volume reading minus 100.0 mL. The density formula is $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass, and $V$ is volume.

Let's assume the final volume readings for A, B, and C are $V_A$, $V_B$, and $V_C$ respectively.

The volume of solid A, $V_{sA}=V_A - 100.0$ mL, density of solid A, $
ho_A=\frac{54.5\ g}{V_A - 100.0\ mL}$

The volume of solid B, $V_{sB}=V_B - 100.0$ mL, density of solid B, $
ho_B=\frac{72.2\ g}{V_B - 100.0\ mL}$

The volume of solid C, $V_{sC}=V_C - 100.0$ mL, density of solid C, $
ho_C=\frac{57.8\ g}{V_C - 100.0\ mL}$

Without the actual volume readings of the graduated - cylinder with the solids added, we cannot calculate the exact densities. But the general steps to rank them are as follows:

1. Calculate the volume of each solid by subtracting the initial volume of water (100.0 mL) from the final volume reading of the graduated - cylinder with the solid added.
2. Use the density formula $

ho=\frac{m}{V}$ to calculate the density of each solid.

1. Rank the densities from highest to lowest or lowest to highest depending on the requirements.

If we assume the final volume readings are $V_A = 130$ mL, $V_B = 140$ mL, $V_C = 125$ mL:

Step1: Calculate the volume of each solid

For sample A:
$V_{sA}=130\ mL - 100.0\ mL=30\ mL$
For sample B:
$V_{sB}=140\ mL - 100.0\ mL = 40\ mL$
For sample C:
$V_{sC}=125\ mL - 100.0\ mL=25\ mL$

Step2: Calculate the density of each solid

For sample A:
$
ho_A=\frac{54.5\ g}{30\ mL}\approx1.82\ g/mL$
For sample B:
$
ho_B=\frac{72.2\ g}{40\ mL}=1.805\ g/mL$
For sample C:
$
ho_C=\frac{57.8\ g}{25\ mL}=2.312\ g/mL$

Step3: Rank the densities

$
ho_C>
ho_A>
ho_B$