Question

the compounds x and y form a complex z in aqueous solution. the molar absorption coefficients of x and z in an aqueous solution are 8500 and 7440 lmol-1cm-1 , respectively, at 490 nm, and 5860 and 10280 lmol-1cm-1 , respectively at 540 nm. an equilibrium solution mixture of x and y transmits (using a cell of 1 cm length) 22.08% and 19.23% of light at 490 nm and 540 nm, respectively. if the absorbance due to y at these wavelengths is negligible, find out the concentrations of x and z in the given equilibrium solution mixture.

Answer 1

The concentrations of compounds X and Z in the equilibrium solution mixture are calculated using the Beer-Lambert Law, given the molar absorption coefficients at two wavelengths, 490 nm and 540 nm, and the measured percentage transmissions. The absorbance at both wavelengths is calculated from the percentage transmissions, leading to a system of equations that can be solved to find the concentrations of X and Z.

Step-by-step explanation:

The student's question involves the calculation of the concentrations of components X and Z in an aqueous solution given the molar absorption coefficients (also known as molar absorptivities or extinction coefficients) at two different wavelengths, 490 nm and 540 nm. The absorbance (A) of a substance can be calculated using the Beer-Lambert Law, A = ε ⋅ c ⋅ l, where ε is the molar absorptivity, c is the molar concentration, and l is the path length of the cuvette, which is usually 1 cm. Hence, the units for ε are typically L mol⁻¹ cm⁻¹.

In this problem, we are given the molar absorption coefficients of X and Z, as well as the percentage transmissions at two different wavelengths. We can use the percentage transmissions to calculate the absorbance values. From the absorbance values and known molar absorptivities, we can set up a system of equations to solve for the concentrations of X and Z. The percentage transmission (T) is related to absorbance by the formula A = -log10(T), where T is the percentage transmission divided by 100.

For example, if the percentage transmission at a certain wavelength is 22.08%, the absorbance (A) can be calculated as A = -log10(0.2208). Once we have the absorbance values for each wavelength, we can use these with the provided molar absorptivities to create equations for each wavelength. Because we have two wavelengths and two unknown concentrations, this yields a system of two equations that can be solved for the concentrations of X and Z.

Answer 2

The concentrations of compounds X and Z in the equilibrium solution mixture are as follows:

- Concentration of X:
`\(3.24 * 10^(-5)\) mol/L`

- Concentration of Z:
`\(5.12 * 10^(-5)\) mol/L`

To determine the concentrations of compounds X and Z in the equilibrium solution mixture, we'll apply the Beer-Lambert Law, which relates the absorbance of a solution to the concentration of the absorbing species. The law is given by:

`\[ A = \varepsilon \cdot c \cdot l \]`

where A is the absorbance,
`\( \varepsilon \)` is the molar absorption coefficient, c is the concentration, and l is the path length of the cell (which is 1 cm in this case).

Given data:

- Molar absorption coefficients of X and Z at 490 nm:
`\( \varepsilon_(X,490) = 8500 \, \text{L mol}^(-1)\text{cm}^(-1) \), \( \varepsilon_(Z,490) = 7440 \, \text{L mol}^(-1)\text{cm}^(-1) \).`

- Molar absorption coefficients of X and Z at 540 nm: \(
`\varepsilon_(X,540) = 5860 \, \text{L mol}^(-1)\text{cm}^(-1) \), \( \varepsilon_(Z,540) = 10280 \, \text{L mol}^(-1)\text{cm}^(-1) \).`

- Transmittance at 490 nm: 22.08%, which means absorbance
`\( A_(490) = -\log(0.2208) \).`

- Transmittance at 540 nm: 19.23%, which means absorbance
`\( A_(540) = -\log(0.1923) \).`

First, we'll calculate the absorbance at each wavelength using the transmittance data. Then, we'll set up a system of linear equations based on the Beer-Lambert Law and solve for the concentrations of X and Z.

Let's calculate the absorbance at 490 nm and 540 nm and then solve for the concentrations.

It seems there was an error in the way I attempted to extract the solution from the function. Let me correct this and recalculate the concentrations of X and Z.