Question

Based on the results of Experiment 1 , if the concentration of \(\mathrm{NO}_{2}^{-}\) in a solution is doubled, then the corrected absorbance of the solution will approximately: A. remain the same. B. halve. C. double. D. quadruple.

Short answer

Question: When the concentration of \(\mathrm{NO}_{2}^{-}\) in a solution is doubled, the corrected absorbance will: A. remain the same B. decrease C. double D. increase by a factor of 4 Answer: C. double

Step-by-step solution

Understanding Beer-Lambert Law

The Beer-Lambert Law states that the absorbance of a solution is proportional to the concentration of the solute. Mathematically, it is expressed as: \(A = \epsilon b c\) where \(A\) is the absorbance, \(\epsilon\) is the molar absorptivity, \(b\) is the path length of the light through the solution, and \(c\) is the concentration of the solute in the solution.

Comparing absorbance when concentration is doubled

Now, let's consider a situation when the concentration is doubled, i.e., the new concentration \(c_{new} = 2c\) Using the Beer-Lambert Law, the absorbance with the new concentration will be: \(A_{new} = \epsilon b c_{new} = \epsilon b (2c)\)

Determining the effect of doubling the concentration

Let's compare the initial absorbance (\(A\), corresponding to concentration \(c\)) with the absorbance when the concentration is doubled (\(A_{new}\)): \(\frac{A_{new}}{A}=\frac{\epsilon b (2c)}{\epsilon b c}\) Simplifying this equation, we get: \(\frac{A_{new}}{A}=2\) This means that when the concentration is doubled, the absorbance is also doubled. Therefore, the correct answer is: C. double.

Key concepts

Chemical Concentration

Chemical concentration is a measure of the amount of a particular substance, referred to as a solute, that is dissolved in a given volume of solvent. It plays a critical role in many chemical reactions and processes, as it can affect reaction rates, equilibrium, and product yield. Understanding solute concentration is fundamental in chemistry and related fields, such as pharmacology and environmental science.

The concentration of a solute can be expressed in various ways, including molarity (moles of solute per liter of solution), molality (moles of solute per kilogram of solvent), and mass percentage (mass of solute divided by total mass of solution, multiplied by 100). These units provide a quantitative way to describe how much solute is present in a solution and are essential for accurately preparing and analyzing solutions.

Relevance to Beer-Lambert Law

When we discuss the Beer-Lambert Law, the concentration is integral because it directly influences the absorbance of light by a solution. A high concentration of a solute will typically result in a greater absorbance, assuming all other factors are constant. This relationship allows scientists to determine unknown concentrations by measuring the absorbance of a solution with a known path length and molar absorptivity.

Absorbance

Absorbance is a measure of how much light is absorbed by a sample as light of a particular wavelength passes through it. In an experimental setting, absorbance is measured using a spectrophotometer, an instrument that shines light through a sample and quantifies how much light is absorbed versus how much passes through.

The concept of absorbance is crucial in many scientific analyses, especially in techniques that involve the identification and quantification of substances within a mixture. In the Beer-Lambert Law, absorbance (A) is given by the equation \(A = \: b \: \: c\), where \(\epsilon\) is the molar absorptivity coefficient, \(b\) is the path length of the light through the solution, and \(c\) is the concentration of the solute. This law implies that absorbance is proportional to the concentration of the absorbing species in the solution, provided that other conditions are kept constant.

Importance in Analytical Chemistry

Using the Beer-Lambert Law, scientists can determine the concentration of a chemical in a solution simply by measuring its absorbance. This method is widely used in laboratories for analysis, as it offers a non-destructive way to analyze solutions and requires only a small amount of sample.

Solute Concentration

The term solute concentration refers specifically to the amount of solute in a given volume of solution. Solute concentration is a critical factor in the study of solutions and solubility, since it can drastically affect the properties of the solution, including boiling point elevation, freezing point depression, and osmotic pressure.

When we talk about solute concentration in the context of the Beer-Lambert Law, we are often concerned with its effect on the absorbance of light. A higher solute concentration means more solute molecules are available to interact with light, potentially absorbing more photons and thus increasing the measured absorbance. It is vital to realize that this proportional relationship assumes that the solution behaves ideally, meaning that the solutes do not interact with each other in a way that changes their individual ability to absorb light.

Application in Spectrophotometry

Spectrophotometry often requires a calibration curve, which is a graphical representation of absorbance versus solute concentration. By plotting known concentrations and their corresponding absorbance values, scientists can interpolate the concentration of an unknown sample based on its absorbance. Therefore, accurate measurement and understanding of solute concentration are necessary for quantifying the amount of substance using absorbance data.