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Magazine Chapter 24: Problem 13
What are the units for absorptivity when the path length is given in centimeters and the concentration is expressed in *(a) parts per million? (b) micrograms per liter? *(c) mass-volume percent? (d) grams per liter?
Short Answer
Expert verified
(a) L路cm鈦宦孤穖g鈦宦�, (b) L路cm鈦宦孤仿礸鈦宦�, (c) L路cm鈦宦孤�10路g鈦宦�, (d) L路cm鈦宦孤穏鈦宦�.
Step by step solution
01
Understanding Absorptivity and Beer-Lambert Law
Absorptivity, also known as the molar absorption coefficient, is used in the Beer-Lambert Law, which is expressed as: \( A = \varepsilon \cdot c \cdot l \), where \( A \) is absorbance, \( \varepsilon \) is absorptivity, \( c \) is concentration, and \( l \) is path length. Absorptivity units depend on concentration and path length units.
02
Converting Parts Per Million (ppm) to Concentration Units
Parts per million (ppm) is a concentration unit expressing mass over volume. 1 ppm equals 1 mg/L. So the concentration \( c \) would be expressed in mg/L. Since path length is in cm, absorptivity \( \varepsilon \) will have the units L路cm鈦宦孤穖g鈦宦�.
03
Converting Micrograms per Liter to Concentration Units
For this concentration unit, we have \( c \) as 碌g/L, which is equivalent to mg/L when converted by dividing by 1000. Therefore, the units for absorptivity \( \varepsilon \) will be L路cm鈦宦孤仿礸鈦宦�.
04
Converting Mass-Volume Percent to Concentration Units
Mass-volume percent is weight per 100 mL. We convert to a common unit by defining 1% m/v as 1 g/100 mL, equivalent to 10 g/L. Therefore, absorptivity \( \varepsilon \) has the units L路cm鈦宦孤�(g/10)鈦宦�.
05
Converting Grams Per Liter to Concentration Units
This is a straightforward unit for concentration expressed directly as g/L. \( \varepsilon \) will have the units L路cm鈦宦孤穏鈦宦� based on concentration in g/L.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Absorptivity
Absorptivity, also referred to as the molar absorption coefficient, is a crucial component of the Beer-Lambert Law. This law is foremost in understanding how light is absorbed by substances. It is expressed with the formula: \[ A = \varepsilon \cdot c \cdot l \]where:
- \( A \) is the absorbance, which measures how much light is absorbed by the solution.
- \( \varepsilon \) is the absorptivity or molar absorption coefficient, defining how strongly a substance absorbs light at a given wavelength.
- \( c \) is the concentration of the solution.
- \( l \) is the path length through which the light passes.
Concentration Units
When measuring concentration, the units determine how to express the quantity of solute in a given volume of solution. Various units can be used, each with specific applications:
- **Parts per million (ppm):** This unit is often used when dealing with very dilute solutions. It expresses mass per volume as mg/L, suitable for environmental and safety data.
- **Micrograms per liter (碌g/L):** This unit is practical for measuring trace elements as it is a more refined measure converted from mg/L by dividing by 1000.
- **Mass-volume percent (% m/v):** This unit expresses mass per 100 mL and is transformed to g/L using the relation, where 1% m/v equals 10 g/L.
- **Grams per liter (g/L):** Represents concentration in terms of direct mass to volume ratio, simple and direct, often used in laboratory contexts.
Path Length
The path length, represented as \( l \) in the Beer-Lambert Law, denotes the distance the light travels through the sample. It is typically expressed in centimeters (cm).
Path length plays a significant role because it directly influences the absorbance of light by the solution.
Path length plays a significant role because it directly influences the absorbance of light by the solution.
- When the path length increases, the light has to travel further, likely resulting in more significant absorption and thus a higher absorbance value.
- Correspondingly, as path length decreases, the absorbance is likely less.
Molar Absorption Coefficient
The molar absorption coefficient, or absorptivity, \( \varepsilon \), is a fundamental factor in the Beer-Lambert Law. It characterizes how a particular solute absorbs light and is unique for each substance at a given wavelength.
This coefficient is significant as it can indicate the likelihood of absorption, determining how well a material can absorb light. When conducting experiments:
This coefficient is significant as it can indicate the likelihood of absorption, determining how well a material can absorb light. When conducting experiments:
- A high molar absorption coefficient indicates considerable absorbance with even small concentrations, suggesting strong interactions with specific wavelengths.
- Conversely, a lower coefficient indicates that the substance requires more concentration to achieve similar levels of absorbance.
