Chapter 2, Problem 109CE

Interpretation Introduction

Interpretation:

The density of the liquid and of the metal slug has to be calculated.

Concept Introduction:

Density:  Density is the relationship between the mass of a substance to its volume.  Density is represented in grams per milliliter $\left(\text{g/mL}\right)$ or grams per cubic centimeter $\left(\text{g/cc}\right)\text{.}$  The formula is,

  $\text{Density=}\frac{\text{Mass}\left(\text{g}\right)}{\text{Volume}\left(\text{mL}\text{or}\text{cc}\right)}$

Answer to Problem 109CE

The density of the metal slug is $\text{2}\text{.7}\text{g/mL}\text{.}$

The density of the liquid is $\text{0}\text{.841}\text{g/mL}\text{.}$

Explanation of Solution

Given,

Liquid in a graduated cylinder is $\text{25}\text{.0}\text{mL}\text{.}$

Empty mass is $\text{85}\text{.450}\text{g}\text{.}$

Mass of metal slug is $\text{15}\text{.454}\text{g}\text{.}$

Total volume is $\text{30}\text{.7}\text{mL}\text{.}$

Total mass of slug and cylinder containing liquid is $\text{125}\text{.934}\text{g}\text{.}$

The volume of slug is calculated as,

  Volume of slug=$\text{Total}\text{volume-Volume}\text{of}\text{liquid}$

  Volume of slug=$\text{30}\text{.7}\text{mL-25}\text{.0}\text{mL}$

  Volume of slug=$\text{5}\text{.7}\text{mL}$

The density of the metal slug is $\text{2}\text{.7}\text{g/mL}\text{.}$

The density of the metal slug is calculated as,

  Density of the metal slug=$\frac{\text{Mass}\left(\text{g}\right)}{\text{Volume}\left(\text{mL}\text{or}\text{cc}\right)}$

  Density of the metal slug=$\frac{\text{15}\text{.454}\text{g}}{\text{5}\text{.7}\text{mL}}$

  Density of the metal slug=$\text{2}\text{.7}\text{g/mL}$

The mass of liquid is calculated as,

  $\begin{array}{l}\text{Mass}\text{of}\text{liquid,}\text{cyclinder}\text{and}\text{slag}\text{=}\text{125}\text{.934}\text{g}\\ \text{Mass}\text{of}\text{slag}\text{=}\left(\text{-}\right)\text{15}\text{.545}\text{g}\\ \text{Mass}\text{of}\text{cylinder}\text{=}\left(\text{-}\right)\underset{\_}{\text{89}\text{.450}\text{g}}\\ \text{Mass}\text{of}\text{liquid}\text{=}\text{21}\text{.030}\text{g}\end{array}$

The density of the liquid is calculated as,

  Density of the liquid=$\frac{\text{Mass}\left(\text{g}\right)}{\text{Volume}\left(\text{mL}\text{or}\text{cc}\right)}$

  Density of the liquid=$\frac{\text{21}\text{.030}\text{g}}{\text{25}\text{.0}\text{mL}}$

  Density of the liquid=$\text{0}\text{.841}\text{g/mL}$

The density of the liquid is $\text{0}\text{.841}\text{g/mL}\text{.}$