Problem 136 - General Chemistry

Question

Convert: a \(7.19 \mu \mathrm{g}\) of cyanocobalamin (vitamin \(\mathrm{B}_{12}\) ) to milligrams b \(104 \mathrm{pm},\) the radius of a sulfur atom, to angstroms c \(0.010 \mathrm{~mm}\), the diameter of a typical blood capillary, to centimeters d) \(0.0605 \mathrm{kPa}\) (the pascal, \(\mathrm{Pa}\), is a unit of pressure) to centipascals

Step-by-Step Solution

Answer

a) 0.00719 mg, b) 1.04 Å, c) 0.001 cm, d) 6050 cPa

Step 1: Convert micrograms to milligrams

Given value is 7.19 micrograms (μg). To convert micrograms to milligrams, divide by 1000 since 1 mg = 1000 μg. Therefore, \[ 7.19 ext{ μg} = \frac{7.19}{1000} \text{ mg} = 0.00719 \text{ mg} \]

Step 2: Convert picometers to angstroms

The given value is 104 picometers (pm). We know that 1 angstrom (Å) = 100 pm. To convert picometers to angstroms, divide the number of picometers by 100.Therefore,\[ 104 \text{ pm} = \frac{104}{100} \text{ Å} = 1.04 \text{ Å} \]

Step 3: Convert millimeters to centimeters

The diameter of the capillary is 0.010 mm. To convert millimeters to centimeters, divide by 10 since 1 cm = 10 mm.Therefore,\[ 0.010 \text{ mm} = \frac{0.010}{10} \text{ cm} = 0.001 \text{ cm} \]

Step 4: Convert kilopascals to centipascals

The given pressure is 0.0605 kilopascals (kPa). First, convert kPa to Pa by multiplying by 1000 (since 1 kPa = 1000 Pa), then convert Pa to cPa by multiplying by 100 (as 1 Pa = 100 cPa).First convert to Pa:\[ 0.0605 \text{ kPa} = 0.0605 \times 1000 \text{ Pa} = 60.5 \text{ Pa} \]Now convert to cPa:\[ 60.5 \text{ Pa} = 60.5 \times 100 \text{ cPa} = 6050 \text{ cPa} \]

Key Concepts

Micrograms to Milligrams

Understanding conversions between units can simplify dealing with measurements in different scales. When converting micrograms (μg) to milligrams (mg), it is important to remember the basic relationship.
- 1 milligram equals 1000 micrograms.
This means that whenever you need to convert micrograms to milligrams, a simple division by 1000 is necessary.
Let's take an example: you have 7.19 micrograms of a substance, such as cyanocobalamin (vitamin B12). To convert this to milligrams: \[ 7.19 ext{ μg} = \frac{7.19}{1000} ext{ mg} = 0.00719 ext{ mg} \]This result highlights that 7.19 micrograms is a very small quantity, only 0.00719 milligrams, illustrating how different units reflect scale.
Being aware of the unit conversion factor will help prevent errors in measurements.

Picometers to Angstroms

The scientific community often uses various units to measure extremely small distances, like the size of atoms or molecules. picometers (pm) and angstroms (Å) are two such units.
A picometer is an incredibly small unit of length, where:

• 1 angstrom is equivalent to 100 picometers.

To convert picometers to angstroms, divide by 100. Consider the radius of a sulfur atom, which is 104 picometers. To convert this value to angstroms:\[ 104 ext{ pm} = \frac{104}{100} ext{ Å} = 1.04 ext{ Å} \]This means that 104 picometers translates to 1.04 angstroms.
This conversion helps scientists and engineers express measurements in more familiar terms, especially in fields like chemistry and physics.

Millimeters to Centimeters

When dealing with everyday measurements, converting millimeters (mm) to centimeters (cm) can be quite useful.
The conversion is based on the relationship that:

• 1 centimeter equals 10 millimeters.

Using this knowledge, you can convert by dividing the millimeter measurement by 10. For example, the diameter of a typical blood capillary is about 0.010 mm. Convert this to centimeters:\[ 0.010 ext{ mm} = \frac{0.010}{10} ext{ cm} = 0.001 ext{ cm} \]Thus, 0.010 millimeters is 0.001 centimeters.
Understanding this conversion is useful in a variety of practical contexts, from tailoring clothes to designing microcomponents.

Kilopascals to Centipascals

Pressure is an important measurement in scientific and engineering disciplines, often requiring conversion between units.
Kilopascals (kPa) and centipascals (cPa) are two such units used for pressure. The conversion process involves:

• First converting kilopascals to pascals, knowing that 1 kilopascal equals 1000 pascals.
• Then converting pascals to centipascals, remembering that 1 pascal equals 100 centipascals.

Let's take a given pressure of 0.0605 kilopascals. First, convert to pascals:\[ 0.0605 ext{ kPa} = 0.0605 imes 1000 ext{ Pa} = 60.5 ext{ Pa} \]Next, convert the result into centipascals:\[ 60.5 ext{ Pa} = 60.5 imes 100 ext{ cPa} = 6050 ext{ cPa} \]Hence, 0.0605 kilopascals is equivalent to 6050 centipascals.
Understanding these conversions is vital, especially in fields like meteorology and engineering, where precise pressure measurements are critical.