To determine the concentration of the original (undiluted) sample, we can follow these steps:
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Understand the dilution factor: You diluted the sample 4x, which means the original concentration is 4 times that of the diluted sample.
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Measure the absorbance of the diluted sample: You measured an absorbance of 0.6 for the diluted sample.
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Use Beer-Lambert Law: The relationship between absorbance (A), concentration (C), and path length (l) is given by the Beer-Lambert Law: \[ A = \varepsilon \cdot C \cdot l \] where \( \varepsilon \) is the molar absorptivity and \( l \) is the path length. Since we are focusing on relative concentrations, we can simplify our calculations assuming the same path length and absorptivity for both the original and diluted samples.
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Calculating the concentration: Let \( C_d \) be the concentration of the diluted sample and \( C_o \) be the concentration of the original sample. The relationship can be written as: \[ C_o = 4 \cdot C_d \]
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Express the diluted concentration in terms of absorbance: The absorbance is proportional to the concentration (if the path length and absorptivity are constant). Thus, for the diluted sample with absorbance \( A_d = 0.6 \): \[ A_d \propto C_d \] This means we can treat the absorbance directly as a relative measure of concentration for this purpose (as long as the effective absorbance range is linear).
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Assuming a proportionality: We assume the absorbance of the diluted sample (A_d) is directly proportional to its concentration: \[ C_d = k \cdot A_d \] We can consider \( k \) to be a constant representing the proportionality for our calculation.
To find \( C_o \): \[ C_d = A_d \quad \text{(in arbitrary units, since we're looking for mg/ml, let's assume)} \] Let's say at an absorbance of 0.6, the diluted concentration \( C_d \) can be simplified to 0.6 mg/ml (since we need to find a numeric factor).
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Calculating \( C_o \): Thus, the original concentration \( C_o \) becomes: \[ C_o = 4 \cdot C_d = 4 \cdot 0.6 \text{ mg/ml} = 2.4 \text{ mg/ml} \]
Therefore, the concentration of the original (undiluted) sample is 2.4 mg/ml.