Chapter 3, Problem 75A

a)

Interpretation Introduction

Interpretation : The units in microliters per second are to be converted.

Concept Introduction : Dimensional analysis is a useful method for resolving conversion issues where measurements in one unit are changed to equal measurements in another.

Answer to Problem 75A

The units in microliters per second is $\text{7}\text{.3}\text{μL/s}$ .

Explanation of Solution

Given information :

The given value is $0.44\text{mL/min}$ .

It is known that $\text{1}\text{L}\text{=}{10}^3\text{mL}$ , $\text{1}\text{L}\text{=}{10}^6\text{μL}$ and $\text{1}\text{min}\text{=}60\text{s}$ .

The desired conversion is $\text{mL/min}\to \text{μL/s}$ .

The conversion of the units is given as

  $\begin{array}{c}0.44\text{mL/min}=\frac{0.44\cancel{\text{mL}}}{1\cancel{\text{min}}}\times \frac{1\cancel{\text{L}}}{{10}^3\cancel{\text{mL}}}\times \frac{{10}^6\text{μL}}{1\cancel{\text{L}}}\times \frac{1\cancel{\text{min}}}{60\text{ s}}\\ =\left(7.3\times {10}^{-3}\right)\times {10}^3\text{μL/s}\\ \text{=7}\text{.3}\text{μL/s}\end{array}$

b)

Interpretation Introduction

Interpretation : The units in milligrams per square millimeter are to be converted.

Concept Introduction : Dimensional analysis is a useful method for resolving conversion issues where measurements in one unit are changed to equal measurements in another.

Answer to Problem 75A

The units in milligram per square millimeter are $7.86\times {10}^1{\text{mg/mm}}^2$ .

Explanation of Solution

Given information :

The given value is $7.86{\text{g/cm}}^2$ .

It is known that $\text{1}{\text{m}}^2\text{=}{\text{10}}^4{\text{cm}}^2$ , $\text{1}{\text{m}}^2\text{=}{\text{10}}^6{\text{mm}}^2$ and $\text{1}\text{g}\text{=}{\text{10}}^3\text{mg}$ .

The desired conversion is ${\text{g/cm}}^2\to {\text{mg/mm}}^2$ .

The conversion of the expression is given as

  $\begin{array}{c}7.86{\text{g/cm}}^2\text{=}\frac{7.86\cancel{\text{g}}}{\cancel{{\text{cm}}^2}}\times \frac{{10}^4\cancel{{\text{cm}}^2}}{1\cancel{{\text{m}}^2}}\times \frac{1\cancel{{\text{m}}^2}}{{10}^6{\text{mm}}^2}\times \frac{{10}^3\text{mg}}{1\cancel{\text{g}}}\left(\because \text{1}{\text{m}}^2\text{=}{\text{10}}^4{\text{cm}}^2,\text{1}{\text{m}}^2\text{=}{\text{10}}^6{\text{mm}}^2,\text{1}\text{g}\text{=}{\text{10}}^3\text{mg}\right)\\ \text{=}7.86\times {10}^1{\text{mg/mm}}^2\end{array}$

c)

Interpretation Introduction

Interpretation : The unit in grams per cubic centimeter is to be converted.

Concept Introduction : Dimensional analysis is a useful method for resolving conversion issues where measurements in one unit are changed to equal measurements in another.

Answer to Problem 75A

The unit in gram per cubic centimeter is $1.54{\text{g/cm}}^3$ .

Explanation of Solution

Given information :

The given value is $1.54\text{kg/L}$ .

It is known that $\text{1}\text{L}\text{=}{10}^3{\text{cm}}^3$ and $\text{1}\text{kg}\text{=}{10}^3\text{g}$ .

The desired conversion is $\text{kg/L}\to {\text{g/cm}}^3$ .

The conversion of the units is given as

  $\begin{array}{c}1.54\text{kg/L}=\frac{1.54\cancel{\text{kg}}}{\cancel{\text{L}}}\times \frac{{10}^3\text{g}}{1\cancel{\text{kg}}}\times \frac{1\cancel{\text{L}}}{{10}^3{\text{cm}}^3}\left(\because \text{1}\text{L}\text{=}{10}^3{\text{cm}}^3,\text{1}\text{kg}\text{=}{10}^3\text{g}\right)\\ =1.54{\text{g/cm}}^3\end{array}$