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Interactive Audio Lesson
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Uncertainty in Titration Data
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Today, we'll start discussing how we should handle uncertainty in our measurements during titrations. Can someone tell me what equivalence volume means?
I think it's the volume of titrant at which the reaction is complete, right?
Exactly! And when we measure this volume multiple times, we can calculate the mean. Let's say we have values of 25.12 mL, 25.08 mL, and 25.10 mL. Who can compute the mean?
The mean would be 25.10 mL!
Great! Now, how do we calculate the uncertainty associated with this mean?
I think we need to calculate the standard deviation first and then the standard error!
Correct! Let's remember the standard error formula: it's the standard deviation divided by the square root of the number of measurements. In this case, we have three measurements, so how would we compute that?
If standard deviation is, say, 0.020 mL, then the standard error would be 0.020 divided by the square root of 3.
Perfect! So our final result for the equivalence volume would be reported as 25.10 plus or minus our uncertainty. Remember, we need to always report uncertainties in a way that's understandable!
Can I get someone to summarize the key things we discussed here?
Sure! We learned how to calculate the mean equivalence volume and the associated uncertainty using standard deviation and error.
Calibration Curve for UV-Vis Spectroscopy
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Now, let’s move on to UV-Vis spectroscopy. Can someone explain what a calibration curve is?
It's a plot of absorbance against concentration of standards to find out the relationship.
Exactly! If we have standard solutions at different concentrations, how do we determine the molar absorptivity from a linear fit?
We fit a straight line through the data points, and the slope will give us the molar absorptivity once we convert concentrations to molarity!
Correct! Don't forget that the path length plays a role here too. If you plot absorbance versus concentration and obtain a slope of, say, 0.102, what’s our next step?
We would then calculate molar absorptivity by converting the concentration units and adjusting for path length.
Well done! Now, if we have an unknown sample with an absorbance of 0.550, how would we find its concentration?
We rearrange our linear equation to find concentration! It’s A = m * C, right? So C would equal A/m.
Exactly! Let’s wrap this up. Can anyone summarize our session today on calibration curves?
We discussed calibration curves, determined the slope for molar absorptivity, and found unknown concentrations using absorbance!
IR Spectroscopy Quantitation
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Next, let's cover IR spectroscopy. Which law relates absorbance to concentration in IR measurements?
That would be Beer’s Law!
Right! If we prepared KBr pellets of different concentrations, how might we assess if Beer’s Law holds?
We can analyze the peak area in the IR spectrum and plot it against concentration!
Exactly! If the plot is linear, then Beer’s Law holds. What are we looking for in the peak area data?
The slope would give us how absorbance changes with concentration, and we can find drug percentages in unknown samples!
Great! Now someone summarize the key takeaways regarding IR quantitation.
We learned that we can assess concentration using peak areas based on Beer’s Law, checking linearity for accuracy!
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
The section emphasizes practical application of key concepts in measurement and data processing, providing integrative examples and practice problems that cover uncertainty in titration data, calibration curves in UV-Vis spectroscopy, infrared spectroscopy quantitation, NMR analysis, and ICP-OES metal concentration assessment.
Detailed
Integrative Examples and Practice Problems
This section provides crucial practice problems that are integral in understanding the principles discussed in previous sections of the chapter on measurement and data processing in chemistry. The problems cover various analytical techniques and uncertainty propagation, allowing students to apply theoretical concepts to real-world scenarios.
Key Topics Covered:
- Uncertainty in Titration Data: Calculation of moles of HCl during titrations and propagating uncertainty using the mean equivalence volume.
- Calibration Curve for UV-Vis Spectroscopy: Understanding a dye's molar absorptivity and conducting subsequent analysis of an unknown sample.
- IR Spectroscopy Quantitation: Evaluating absorption peak areas to determine drug concentration and understanding Beer’s law applicability.
- NMR Quantitative Analysis: Utilizing integrals in NMR spectra to derive concentrations of compounds and understanding the concept of internal standards.
- ICP-OES Analysis of Metal Concentration: Analyzing emission intensities from standards to quantify unknown samples.
All exercises encourage critical thinking in data treatment, emphasizing the importance of accurate reporting and uncertainty management in analytical chemistry.
Audio Book
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4.1 Uncertainty in Titration Data
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You titrate 25.00 mL of 0.1000 M HCl with 0.1000 M NaOH. You perform three replicates and obtain equivalence volumes (Ve) of 25.12 mL, 25.08 mL, and 25.10 mL. Compute:
1. Mean equivalence volume and its uncertainty
2. Moles of HCl in each titration
3. Average moles of HCl and uncertainty
4. Concentration of HCl with propagated uncertainty
Solution Sketch:
● Mean Ve = (25.12 + 25.08 + 25.10) ÷ 3 = 25.10 mL.
● Sample standard deviation s = sqrt [ Σ (Vᵢ – V̄ )² ÷ (N – 1) ] = sqrt[( (0.02)² + (0.02)² + (0.00)² ) ÷ 2 ] = sqrt[(0.0004 + 0.0004) ÷ 2] = sqrt(0.0004) = 0.020 mL.
● Standard error σ_V̄ = s ÷ sqrt(3) = 0.020 ÷ 1.732 = 0.0115 mL.
● Report Ve = (25.10 ± 0.012) mL.
● Moles HCl each titration = M_NaOH × Ve (in L) = 0.1000 M × 0.02510 L = 0.002510 mol.
● Uncertainty in moles due to Ve uncertainty: δn = 0.1000 M × 0.000012 L = 1.20 × 10⁻⁶ mol.
● Concentration HCl = (average moles HCl) ÷ (0.02500 L). Average moles = 0.002510 ± 0.0000012 mol.
● Concentration c = 0.002510 ÷ 0.02500 = 0.10040 M.
● Propagate uncertainty: relative uncertainty in moles = 1.20×10⁻⁶ ÷ 0.002510 = 0.000478 = 0.0478%. Relative uncertainty in volume (25.00 mL pipet) assume ±0.02 mL (manufacturer spec). Relative uncertainty = 0.02 ÷ 25.00 = 0.0008 = 0.08%. Combined relative uncertainty in concentration = sqrt(0.0478%² + 0.08%²) = sqrt((0.000478)² + (0.000800)²) = sqrt(2.29×10⁻⁷ + 6.40×10⁻⁷) = sqrt(8.69×10⁻⁷) = 0.000932 = 0.0932%.
● Absolute uncertainty in c = 0.10040 × 0.000932 = 0.000094.
● Final: [HCl] = (0.10040 ± 0.00009) M.
Detailed Explanation
This chunk discusses how to handle uncertainty in measurements for a titration experiment in chemistry. It breaks down the process into key steps: First, we calculate the mean equilibrium volume from the three replicates. Next, we calculate the standard deviation to assess variability among the measurements. By then figuring out the uncertainty in the mean volume, we can derive the number of moles of HCl present in the titration. Finally, applying these results allows us to compute the precise concentration of HCl along with its propagated uncertainty, showing how each step slots together to ensure reliable results in experimental science.
Examples & Analogies
Imagine you're a baker trying to make a cake with perfect ingredients. Each time, you measure flour a little differently, leading to slight variations in your mix. Just as a baker needs to find an average amount of flour used and account for the small variations to get the best cake, chemists measure their solutions carefully and average measures to ensure the final result is as accurate as possible, adjusting for any small errors in measurement.
4.2 Calibration Curve for UV-Vis Spectroscopy
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A dye has λ_max at 520 nm. You prepare standard solutions at concentrations 1.00, 2.00, 4.00, 6.00, and 8.00 mg/L. Measured absorbance at 520 nm (with 1.00 cm path length) are 0.102, 0.204, 0.407, 0.610, and 0.812. Construct a calibration curve and determine molar absorptivity ε if molar mass of dye is 300 g/mol. Then determine concentration of an unknown sample whose absorbance is 0.550. Include uncertainty propagation if each absorbance reading has ±0.003 uncertainty.
Solution Sketch:
● Plot A versus c (mg/L). Fit linear regression: slope m (units absorbance per mg/L), intercept b. Since data look perfectly linear (doubling c doubles A), intercept b ≈ 0.000.
● Using least‐squares (or by eyeballing), slope m ≈ A / c = 0.102/1.00 = 0.102 absorbance per mg/L. Check residuals: each absorbance is exactly 0.102 × c.
● Therefore calibration equation: A = (0.102 ± δm) × c. Determine δm from regression (since measurement errors ±0.003). Using standard linear regression formulas, slope uncertainty δm ≈ 0.0002.
● Convert slope to ε: c (mg/L) → mol/L by dividing by 10^3 mg/g × 300 g/mol = c_mol/L = (c_mg/L) ÷ (300,000 mg/mol). So 1 mg/L = (1 ÷ 300,000) mol/L = 3.333×10⁻⁶ M.
● A = m × c_mg/L = ε × ℓ × c_mol/L. Hence ε = (m × c_mg/L) ÷ c_mol/L ÷ ℓ = m ÷ (3.333×10⁻⁶ M) ÷ 1.00 cm = (0.102) ÷ 3.333×10⁻⁶ = 30,600 L mol⁻¹ cm⁻¹. Uncertainty in ε = δm ÷ 3.333×10⁻⁶ = 0.0002 ÷ 3.333×10⁻⁶ = 60 L mol⁻¹ cm⁻¹.
● Unknown A = 0.550 ± 0.003 → c_mg/L = A ÷ m = 0.550 ÷ 0.102 = 5.392 mg/L. Propagate uncertainty: δc = sqrt[ (δA / m)² + (A δm / m²)² ] = sqrt[ (0.003 / 0.102)² + (0.550 × 0.0002 / 0.102²)² ] = sqrt[ (0.02941)² + ( (0.00011) / 0.010404 )² ] = sqrt[ (0.000865) + (0.01058)² ] = sqrt(0.000865 + 0.000112 ) = sqrt(0.000977 ) = 0.0313 mg/L.
● Convert to mol/L: c_mol/L = 5.392 mg/L × 3.333×10⁻⁶ mol/mg = 1.797×10⁻⁵ M;
δc_mol/L = 0.0313 mg/L × 3.333×10⁻⁶ = 1.043×10⁻⁷ M.
● Final: c = (1.797 ± 0.104) × 10⁻⁵ M.
Detailed Explanation
This chunk elaborates on constructing a calibration curve for UV-Vis spectroscopy measurements. It starts with preparing a range of standard solutions and measuring their absorbance at the dye’s maximum wavelength (λ_max). By plotting absorbance against concentration, we can derive a slope for the linear relationship, which allows us to apply Beer's Law. Moreover, it incorporates uncertainty analysis, considering uncertainties in both the absorbance readings and slope to arrive at the molar absorptivity of the dye and to find the concentration of an unknown sample, demonstrating how each piece of the analysis builds on the previous one for conclusive results.
Examples & Analogies
Think of a calibration curve as a map for finding your way to a treasure. Each marked path (concentration of dye) leads you to a specific spot (absorbance). When you follow the map (plot the data), you establish a relationship that tells you where to dig (find the concentration of the unknown). Just as you’d want to measure distances accurately to ensure you land on the treasure, carefully measuring absorbance and accounting for uncertainties helps ensure your scientific conclusions are spot on.
4.3 IR Spectroscopy Quantitation
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A pharmaceutical compound has a characteristic C=O stretch at 1700 cm⁻¹. You prepare KBr pellets with 0.5%, 1.0%, 1.5%, 2.0%, and 2.5% (wt/wt) of drug in KBr. FTIR absorption peak areas at 1700 cm⁻¹ are 0.152, 0.305, 0.459, 0.610, and 0.762 arbitrary units (AU). Determine if Beer’s law holds (A ∝ concentration). If yes, find slope. An unknown pellet shows peak area 0.524 AU. Calculate drug percentage in pellet. Assume ±0.005 AU uncertainty in area.
Solution Sketch:
● Plot peak area (y) versus % drug (x). Check linearity: each 0.5% increase → ~0.152 AU increase. Slope ≈ 0.152 ÷ 0.5% = 0.304 AU per %. Confirm each point matches: 2.0% → 0.610 (within rounding).
● Linear regression yields slope m = 0.305 ± 0.003 AU/%.● Equation: A = (0.305) × (% drug) + b; intercept b ≈ 0 (check: 0.5% gives 0.152, so b = 0.152 – 0.305×0.5 = 0.152 – 0.1525 = –0.0005, essentially zero).
● Unknown A = 0.524 ± 0.005 AU → % drug = A ÷ m = 0.524 ÷ 0.305 = 1.717%. Propagate uncertainty: δ(% drug) = sqrt[ (δA / m)² + (A δm / m²)² ] = sqrt[ (0.005 / 0.305)² + (0.524 × 0.003 / 0.305²)² ] = sqrt[ (0.01639)² + ( (0.001572) / 0.093025 )² ] = sqrt[ (0.000269 + 0.01691)² ] = sqrt(0.000269 + 0.000286) = sqrt(0.000555) = 0.0236%.
● Report: (1.717 ± 0.024) % (wt/wt).
Detailed Explanation
This chunk focuses on the quantitation of a pharmaceutical compound using Infrared (IR) spectroscopy. It explains how to prepare a series of standard KBr pellets with known concentrations of the drug and measure the corresponding absorption peak areas at a specific wavelength. By plotting these values, we can determine if there’s a linear relationship confirming Beer’s Law is valid. The slope gives us a conversion factor for analyzing unknown samples, allowing us to ascertain the drug concentration and also calculate the associated uncertainty, highlighting the rigor of quantitative analysis in spectroscopy.
Examples & Analogies
Imagine you're baking cookies with a friend's recipe and want to see how much chocolate to add for a perfect taste. By testing small batches (KBr pellets), you gauge how the amount of chocolate (concentration) affects the sweetness (absorbance). By plotting your test results on a chart, you can figure out the exact amount needed for the next batch (quantitating the unknown sample). Just like in cooking, accurate measurements and understanding the relationship between ingredients lead to the best outcome.
4.4 NMR Quantitative Analysis
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You dissolve 10.00 mg of a pure internal standard (p-xylene) in 1.000 g of sample containing unknown concentration of benzene. In the ¹H NMR spectrum (400 MHz, CDCl₃), the four aromatic protons of p-xylene appear as a singlet at 2.29 ppm (integral = 4.00), and the six aromatic protons of benzene appear as a singlet at 7.36 ppm (integral = 6.00). Determine concentration (mass fraction) of benzene. Molar mass p-xylene = 106 g/mol; benzene = 78.11 g/mol. Assume uncertainties in integrals ±0.02 and sample mass ±0.001 g.
Solution Sketch:
● Moles of internal standard: 10.00 mg ÷ 106 g/mol = 9.433×10⁻⁵ mol.
● Integral of 4 protons (p-xylene) = 4.00 ± 0.02; so area per proton = 4.00 ÷ 4 = 1.000 ± 0.005.
● Integral of 6 protons (benzene) = 6.00 ± 0.02; so area per proton = 6.00 ÷ 6 = 1.000 ± 0.0033.
● Since area per proton is equal (1.000), moles of benzene protons = (integral per proton ratio) × (moles of p-xylene protons). But more straightforward:
○ Total integral for p-xylene peaks = 4.00; corresponds to 9.433×10⁻⁵ mol p-xylene molecules × 4 protons each = 3.773×10⁻⁴ mol protons.
○ Since area is proportional to moles of protons, each integral unit corresponds to (3.773×10⁻⁴) ÷ 4.00 = 9.433×10⁻⁵ mol of protons per integral unit.
○ For benzene, integral = 6.00 units corresponds to 6.00 × (9.433×10⁻⁵) = 5.660×10⁻⁴ mol of protons. But benzene has 6 protons per molecule, so moles of benzene molecules = (5.660×10⁻⁴) ÷ 6 = 9.433×10⁻⁵ mol (same as p-xylene).
○ Moles benzene = 9.433×10⁻⁵ mol; mass of benzene = moles × 78.11 g/mol = 0.007365 g = 7.365 mg.
● Total sample mass = 1.000 g = 1000 mg (internal standard + benzene + other sample matrix). If sample contains only benzene + internal standard, total mass = 10 mg + 7.365 mg = 17.365 mg. But the problem likely implies that 1.000 g of sample contains unknown benzene plus 10 mg standard. If so, mass of benzene in 1.000 g sample = 7.365 mg; mass fraction = 7.365 mg ÷ 1000 mg = 0.007365 (0.7365%).
● Propagate uncertainty: integral uncertainties ±0.02 in each. Calculate fractional uncertainty in moles benzene:
○ Uncertainty in area per proton of p-xylene: (0.02 ÷ 4) = 0.005. Fractional = 0.005 ÷ 1.000 = 0.005.
○ Uncertainty in area per proton of benzene: (0.02 ÷ 6) = 0.00333. Fractional = 0.00333 ÷ 1.000 = 0.00333.
○ Total fractional uncertainty in ratio of integrals assuming uncorrelated: sqrt(0.005² + 0.00333²) = sqrt(2.5×10⁻⁵ + 1.11×10⁻⁵) = sqrt(3.61×10⁻⁵) = 0.00601 = 0.601%.
○ Uncertainty in moles benzene = 0.00601 × 9.433×10⁻⁵ mol = 5.67×10⁻⁷ mol.
○ Uncertainty in mass benzene = 5.67×10⁻⁷ mol × 78.11 g/mol = 4.43×10⁻⁵ g = 0.0443 mg.
○ Uncertainty in mass fraction = 0.0443 mg ÷ 1000 mg = 4.43×10⁻⁵ = 0.00443%.
● Final: benzene mass fraction = 0.7365% ± 0.0044%.
Detailed Explanation
This chunk deals with quantifying the concentration of benzene using NMR spectroscopy by employing a known internal standard, p-xylene. It details how to interpret NMR integrals for both the standard and the unknown, allowing a comparison of proton counts to deduce the amount of benzene present. Calculations follow to convert moles into grams based on molar masses, followed by assessing the total mass fraction of benzene in the original sample. It also showcases how uncertainty analysis plays a critical role in the final concentration estimation, reflecting the precision needed in scientific calculations.
Examples & Analogies
Consider a cooking scenario where you're using a spoon (internal standard) to measure out sugar (benzene). If you know the exact weight of the spoon, you can use that reference to determine how much sugar is in your recipe by comparing how full the spoon is after it’s dipped into the sugar jar. Here, the spoon's weight is constant, and every dip (integral) tells you how much sugar you’ve added. This allows for accuracy in your sweetening experience, just as NMR helps scientists get precise measurements by comparing known standards to unknown samples.
4.5 ICP-OES Analysis of Metal Concentration
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In an ICP-OES run, you measure emission intensities for two standards and an unknown for element X at wavelength λ. Standards: 1.00 ppm X → 1250 counts; 5.00 ppm X → 6200 counts. Unknown sample gives 3100 counts. Determine X concentration in sample. Assume ±2 counts uncertainty in intensity and ±0.02 ppm uncertainty in standard concentrations.
Solution Sketch:
● Fit linear regression through points (1.00, 1250) and (5.00, 6200). Slope m = (6200 – 1250) ÷ (5.00 – 1.00) = 4950 ÷ 4.00 = 1237.5 counts per ppm. Intercept b = 1250 – 1237.5 × 1.00 = 12.5 counts.
● Calibration eqn: I = 1237.5 × c + 12.5.
● Solve for c_unknown: c = (I_unknown – b) ÷ m = (3100 – 12.5) ÷ 1237.5 = 3087.5 ÷ 1237.5 ≈ 2.495 ppm.
Uncertainty Propagation:
● Uncertainties: δI_unknown = ±2 counts; δm from slope uncertainty; δb from intercept uncertainty. But with only two standards, uncertainty in slope can be estimated from 2-point fit:
○ Suppose standard intensities have δI_std = ±2 and δc_std = ±0.02; propagate to slope uncertainty:
■ m = (I₂ – I₁) ÷ (c₂ – c₁). Uncertainty δm = sqrt [ (δI₂² + δI₁²) ÷ (c₂ – c₁)² + ((I₂ – I₁)² × (δc₂² + δc₁²)) ÷ (c₂ – c₁)⁴ ). ]
■ δI₂ = δI₁ = 2 counts. δc₂ = δc₁ = 0.02 ppm.
■ Numerator part from intensities: (2² + 2²) ÷ 4² = (4 + 4) ÷ 16 = 8 ÷ 16 = 0.5.
■ Numerator part from concentrations: ( (6200 – 1250)² × (0.02² + 0.02²) ) ÷ 4⁴ = (4950² × (0.0004 + 0.0004)) ÷ 256 = (24,502,500 × 0.0008) ÷ 256 = 19,602.0 ÷ 256 = 76.57.
■ Sum = 0.5 + 76.57 = 77.07. δm = sqrt(77.07) = 8.78 counts/ppm.
● Intercept uncertainty δb = sqrt [ (δI₁)² + (c₁² δm²) + (m² δc₁²) ] (propagate b = I₁ – m c₁).
○ δI₁ = 2; c₁ = 1.00; δm = 8.78; m = 1237.5; δc₁ = 0.02.
○ Terms: δI₁² = 4; (c₁ δm)² = (1×8.78)² = 77.07; (m δc₁)² = (1237.5 × 0.02)² = (24.75)² = 612.6. Sum = 4 + 77.07 + 612.6 = 693.7. δb = sqrt(693.7) = 26.34 counts.
● Now c_unknown = (I_unknown – b) ÷ m. Propagate uncertainty δc:
○ ∂c/∂I_unknown = 1 ÷ m
○ ∂c/∂b = –1 ÷ m
○ ∂c/∂m = – (I_unknown – b) ÷ m² = –(3100 – 12.5) ÷ (1237.5²) = –3087.5 ÷ 1,531,640.6 = –0.002016.
● δc = sqrt [ ( (1/m) δI_unknown )² + ( (–1/m) δb )² + ( (–(I_unknown – b)/m²) δm )² ].
○ (1/m) δI_unknown = (1/1237.5) × 2 = 0.001617 ppm. Squared = 2.614×10⁻⁶.
○ (–1/m) δb = (–1/1237.5) × 26.34 = –0.02128 ppm. Squared = 0.000453.
○ (–(I_unknown – b)/m²) δm = ( –3087.5 ÷ 1,531,640.6 ) × 8.78 = –0.01771 ppm. Squared = 0.000314.
● Sum = 2.614×10⁻⁶ + 0.000453 + 0.000314 = 0.0007696. δc = sqrt(0.0007696) = 0.0277 ppm.
● Final: c_unknown = 2.495 ± 0.028 ppm.
Detailed Explanation
This portion outlines how to determine the concentration of a metal in a sample using Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES). After measuring the emission intensities of two standards, we fit a linear model to establish a relationship between concentration and detected counts. This allows us to extrapolate the concentration of the unknown sample. The process includes analyzing and propagating uncertainties associated with both the standards and the measurements, ensuring the reliability and accuracy of results. Each step is crucial for correct data interpretation in analytical chemistry.
Examples & Analogies
Think of this process like tuning a musical instrument. Each note (emission count) corresponds to a specific pitch (concentration of metal). By playing notes at specific references (the standards) and adjusting based on how they sound, you can determine the pitch of an unknown note. Like adjusting your tuning until it’s just right, analyzing the emission intensities with careful calculations ensures that the estimated concentration aligns accurately with reality.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Calibration Curve: A graphical representation that shows the relationship between absorbance and concentration in spectroscopy.
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Mean Equivalence Volume: The average volume of titrant required to neutralize an acid.
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Molar Absorptivity: A constant that reflects the degree to which a chemical species can absorb light at a particular wavelength.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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Example of calculating mean equivalence volume from three titration results.
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Example of constructing a calibration curve from absorbance values of known concentrations.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎯 Super Acronyms
Use the acronym 'MUC' to remember
🎵 Rhymes Time
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In the lab we measure right,
📖 Fascinating Stories
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Imagine you are in a chemistry lab conducting titrations with friends. You all contribute to the data, learning how to handle measurement uncertainties together, creating a calibration curve that reveals the beauty of science in teamwork.
🧠 Other Memory Gems
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Remember the phrase 'Always Be Measuring' to recall:
Flash Cards
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Glossary of Terms
Review the Definitions for terms.
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Term: Mean Equivalence Volume
Definition:
The average volume of titrant used to reach the equivalence point in titrations.
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Term: Molar Absorptivity
Definition:
A measure of how strongly a chemical species absorbs light at a given wavelength, expressed in L mol⁻¹ cm⁻¹.
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Term: Standard Deviation
Definition:
A statistic measuring the dispersion or spread of a set of values from their mean.
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Term: Beer’s Law
Definition:
A law stating that the absorbance of a substance is directly proportional to its concentration and path length.