Question

in science, one frequently needs to use conversion factors to change from one unit to another. for example, say you wanted to convert 10,000 cm to meters. you know 100 cm = 1 meter; therefore, 1 m/100 cm = 1. so, to do that conversion: 10,000 cm × 1 meter/100 cm = 100 meters. set up the fraction so that the units cancel to leave meters. this technique will be used extensively later in the course when we calculate molar concentrations, percent concentrations, and number of molecules in solutions. 3. convert the following to ml (assume the liquid is water and that the density of water is 1 g/cm³ = 1 g/ml) (1 pt) a. 1 l b. 0.78 μl c. 60 cm³ d. 5.6 kg e. 10 μl

Explanation:

Part a: Convert 1 L to mL

Step1: Recall the conversion factor

We know that \( 1\space L = 1000\space mL \).

Step2: Apply the conversion factor

To convert \( 1\space L \) to \( mL \), we multiply by the conversion factor: \( 1\space L\times\frac{1000\space mL}{1\space L} \)
The \( L \) units cancel out, leaving \( 1\times1000\space mL = 1000\space mL \).

Step1: Recall the conversion factor

We know that \( 1\space \mu L=10^{- 6}\space L \) and \( 1\space L = 1000\space mL \). First, convert \( \mu L \) to \( L \), then \( L \) to \( mL \).

Step2: Convert \( \mu L \) to \( L \)

\( 0.78\space \mu L=0.78\times10^{-6}\space L = 7.8\times 10^{-7}\space L \)

Step3: Convert \( L \) to \( mL \)

Multiply by the conversion factor \( \frac{1000\space mL}{1\space L} \): \( 7.8\times 10^{-7}\space L\times\frac{1000\space mL}{1\space L}=7.8\times 10^{-4}\space mL = 0.00078\space mL \)

Step1: Recall the relationship between \( cm^{3} \) and \( mL \)

For water (and for most liquids in terms of volume measurement), \( 1\space cm^{3}=1\space mL \)

Step2: Apply the conversion

Since \( 1\space cm^{3} = 1\space mL \), then \( 60\space cm^{3}=60\times1\space mL = 60\space mL \)

Answer:

\( 1000\space mL \)

Part b: Convert \( 0.78\space \mu L \) to mL