To create a calibration curve based on the data provided, we will plot the concentration of the standard solutions (ppm) against their respective absorbance values. Given the linear relationship observed in spectrophotometric analysis due to Beer-Lambert Law, we can expect that the relationship between concentration and absorbance will form a straight line.
Calibration Data
| No. | Concentration (ppm) | Absorbance | |-----|---------------------|------------| | 1 | 1.5 | 0.15 | | 2 | 2.0 | 0.30 | | 3 | 2.5 | 0.45 | | 4 | 3.0 | 0.60 | | 5 | 3.5 | 0.75 | | 6 | 4.0 | 0.90 | | 7 | 4.5 | 1.05 |
Steps to Create the Calibration Curve:
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Plot the Data: On a graph, set the x-axis as the concentration (ppm) and the y-axis as the absorbance. Plot each (Concentration, Absorbance) pair from the data.
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Fit a Line: Using the data points, fit a linear regression line. The equation of the line will generally have the form: \[ \text{Absorbance} = m \times \text{Conc.} + b \] Where:
- \( m \) is the slope of the line,
- \( b \) is the y-intercept.
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Calculate Slope and Intercept: Given the points you have, we can calculate the slope (m) and y-intercept (b). From the data, the slope can be calculated as: \[ m = \frac{\Delta y}{\Delta x} = \frac{(1.05 - 0.15)}{(4.5 - 1.5)} = \frac{0.90}{3} = 0.30 \] The y-intercept (b) can be calculated from one of the points: Using point (1.5, 0.15): \[ 0.15 = 0.30 \cdot 1.5 + b \implies b = 0.15 - 0.45 = -0.30 \]
The equation of the line (calibration curve) is: \[ \text{Absorbance} = 0.30 \times \text{Concentration (ppm)} - 0.30 \]
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Determine Unknown Concentration: To find the concentration of the analyte from its absorbance, rearrange the equation to solve for concentration: \[ \text{Concentration (ppm)} = \frac{\text{Absorbance} + 0.30}{0.30} \]
If an unknown sample's absorbance were measured (let's say it was \(0.75\)), we would substitute: \[ \text{Concentration (ppm)} = \frac{0.75 + 0.30}{0.30} = \frac{1.05}{0.30} = 3.5 \text{ ppm} \]
Summary
- The linear relationship established between concentration and absorbance allows for quick calculations to determine the concentration of unknown samples by measuring their absorbance.
- It is essential to generate a proper calibration curve each time an analysis is performed to ensure accuracy.
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