To determine the concentration of the unknown nitrate-nitrogen solution, you can use Beer-Lambert's Law, which states:
\[ A = \epsilon \cdot c \cdot l \]
Where:
- \( A \) = absorbance
- \( \epsilon \) = molar absorptivity (a constant for the particular substance and wavelength)
- \( c \) = concentration of the solution (in ppm or mol/L)
- \( l \) = path length of the cuvette (usually in centimeters)
Assuming the path length \( l \) is constant and the molar absorptivity \( \epsilon \) remains the same for both the standard and the unknown solution, we can use the ratio of absorbances to find the concentration of the unknown solution.
Given:
- Absorbance of standard solution \( A_s = 0.20 \) (for 1.0 ppm)
- Absorbance of unknown solution \( A_u = 0.15 \)
Using the relationship between absorbance and concentration:
\[ \frac{A_u}{A_s} = \frac{c_u}{c_s} \]
Where:
- \( c_u \) = concentration of the unknown
- \( c_s = 1.0 \) ppm (concentration of the standard)
Substituting the known values into the equation:
\[ \frac{0.15}{0.20} = \frac{c_u}{1.0} \]
Now, solve for \( c_u \):
\[ c_u = 1.0 \times \frac{0.15}{0.20} \]
\[ c_u = 1.0 \times 0.75 = 0.75 , \text{ppm} \]
Thus, the concentration of the unknown nitrate-nitrogen solution is 0.75 ppm.