An impurity in water has an extinction coefficient of 3.45⨉10³ M^-1 cm^-1 at 280 nm, its absorption maximum (A Closer Look, p. 576). Below 50 ppb, the impurity is not a problem for human health. Given that most spectrometers cannot detect absorbances less than 0.0001 with good reliability, is measuring the absorbance of a water sample at 280 nm a good way to detect concentrations of the impurity above the 50-ppb threshold?

Verified step by step guidance

1. Convert the concentration from parts per billion (ppb) to molarity (M). Assume the density of water is 1 g/mL for the conversion.
2. Use the Beer-Lambert Law, which is given by the equation: A = \varepsilon c l, where A is the absorbance, \varepsilon is the extinction coefficient, c is the concentration in molarity, and l is the path length in cm.
3. Substitute the given extinction coefficient (\varepsilon = 3.45 \times 10^3 \text{ M}^{-1} \text{ cm}^{-1}) and the minimum detectable absorbance (A = 0.0001) into the Beer-Lambert Law equation.
4. Assume a typical path length (l) of 1 cm for the spectrometer and solve for the concentration (c) that corresponds to the minimum detectable absorbance.
5. Compare the calculated concentration (c) with the concentration equivalent to 50 ppb to determine if the spectrometer can reliably detect concentrations above the 50-ppb threshold.

Key Concepts

Extinction Coefficient

The extinction coefficient is a measure of how strongly a substance absorbs light at a specific wavelength, expressed in units of M^-1 cm^-1. It indicates the amount of light absorbed per unit concentration of the substance in a solution. A higher extinction coefficient means that even small concentrations of the substance can lead to significant absorbance, making it easier to detect.

Absorbance and Beer-Lambert Law

Absorbance is a logarithmic measure of the amount of light absorbed by a sample, defined by the Beer-Lambert Law, which states that absorbance (A) is directly proportional to the concentration (c) of the absorbing species and the path length (l) of the light through the sample. This relationship allows for the calculation of concentration from measured absorbance, provided the extinction coefficient is known.

Detection Limit

The detection limit is the lowest concentration of a substance that can be reliably detected by an analytical method, often defined by the minimum absorbance that can be measured with acceptable precision. In this context, if the detection limit of the spectrometer is 0.0001 absorbance, it is crucial to determine whether the absorbance corresponding to the 50 ppb threshold of the impurity exceeds this limit for effective detection.