Q.2.56 - An Introduction to General, Organic, and Biological Chemistry

Question

Perform each of the following conversions using metric conversion factors: 

a. $4.82 \times {10}^{-5}$ L to picoliters 

b. $575.2$ dm to kilometers 

c. $5 \times {10}^{-4}$ kg to micrograms 

d. $6.4 \times {10}^{10}$ ps to seconds 

Step-by-Step Solution

Answer

a. $4.82 \times {10}^7 \mathrm{pL}$

b. $0.0572 \mathrm{Km}$

c. $500 \mathrm{mg}$

d. $6.4\times {10}^{-2} s$$6.4\times {10}^{-2} \mathrm{s}$

Step 1: Given Information

Unit conversion for L to pL

Step 2: Part (a) Explanation

The unit conversion of L into pL can be given as:

$1 \mathrm{L}= {10}^{12 }\mathrm{pL}$

So, $4.82\times {10}^{-5} \mathrm{L}$will be

$4.82\times {10}^{-5}L=4.82\times {10}^{-5}\times {10}^{12}=4.82\times {10}^7 pL$

Step 1: Part (b) Given Information

Unit conversion of dm into Km

Step 2: Part (b) Explanation

The unit conversion for dm into Km can be given as:

So, 575.2 dm will be

$575.5 \mathrm{dm}=575.2\times 0.1=0.0572 \mathrm{Km}$

Step 1: Part (c) Given Information

Unit conversion of Kg into mg

Step 2: Part (c) Explanation

The unit conversion of Kg into mg can be given as:

$1 Kg={10}^6 mg$

So, $5\times {10}^{-4} Kg$ will be

$$\begin{gathered} 5\times {10}^{-4} Kg=5\times {10}^{-4}\times {10}^6=5\times {10}^2 mg \\ or \\ 500 mg \end{gathered}$$

Step 1: Part (d) Given Information

Unit conversion of ps into s

Step 2: Part (d) Explanation

The unit conversion of picoseconds into seconds can be given as:

$1 ps={10}^{-12} s$

So,$6.4\times {10}^{10}ps=6.4\times {10}^{10}\times {10}^{-12}=6.4\times {10}^{-2} s$