Question

The molar extinction coefficient of a compound, X, at 370 nm wavelength is 250 m^2 mol^-1. It's solutions of concentration 7.5 * 10^-2 mol m^-3 is taken in a cell of thickness 0.010 m. Find the ratio of the intensity of transmitted radiation to the intensity of the incident radiation.

Answer 1

Answer on Question #51537 – Chemistry – Physical Chemistry

Question

The molar extinction coefficient of a compound, X, at 370 nm wavelength is $250\,\mathrm{m}^2\,\mathrm{mol}^{-1}$. It's solutions of concentration $7.5 \cdot 10^{-2}\,\mathrm{mol}\,\mathrm{m}^{-3}$ is taken in a cell of thickness $0.010\,\mathrm{m}$. Find the ratio of the intensity of transmitted radiation to the intensity of the incident radiation.

Solution:

According to the Beer-Lambert law:

$$\log_{10} \frac{I_0}{I} = \varepsilon \cdot l \cdot c$$

- $I_0$ - the intensity of the incident radiation

- $l$ - the intensity of transmitted radiation

- $\varepsilon$ - molar extinction coefficient

- $l$ - cell thickness

- $c$ - concentration

The ratio of the intensity of transmitted radiation to the intensity of the incident radiation is:

$$\frac{I_0}{I} = 10^{\varepsilon \cdot l \cdot c}$$ $$\frac{I}{I_0} = 10^{-\varepsilon \cdot l \cdot c}$$ $$\frac{I}{I_0} = 10^{-(250\,\mathrm{m}^2\,\mathrm{mol}^{-1} \cdot 7.5 \cdot 10^{-2}\,\mathrm{mol} \cdot \mathrm{m}^{-3} \cdot 0.010\,\mathrm{m})} = 10^{-0.1875} = 0.65$$

Answer: 0.65

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