A student based the analysis of Cu(II) in a sample on the formation of the blue complex [Cu(H2O)6]+2. A standard solution was made when 1.276g of pure copper wire (MM= 63.546g/mol) was weighed, dissolved in concentrated HNO3, and diluted to 1.00x102mL.
The stock solution was used to make a dilution by mixing 4.00mL of stock solution with 46.0mL of deionized water. Colorimetric determination gave that the absorbance of the sample was 0.1776 when the path length of the light through the solution was exactly 1cm.
Calculate the transmittance of the solution.
what is the answer??
To calculate the transmittance of the solution, we need to first calculate the absorbance using Beer-Lambert's Law, and then use the formula for transmittance.
1. Calculate the molar concentration of Cu(II) in the stock solution:
- We know that the molar mass of copper wire is 63.546 g/mol and the mass of the copper wire used is 1.276 g.
- Divide the mass of copper wire used by the molar mass to obtain the number of moles: 1.276 g / 63.546 g/mol = 0.0201 mol.
- Now, divide the number of moles by the volume of the stock solution in liters (converted from mL): 0.0201 mol / (1.00 x 10^2 mL / 1000 mL/L) = 0.201 M.
2. Calculate the concentration of Cu(II) in the diluted solution:
- We know that 4.00 mL of the stock solution was mixed with 46.0 mL of deionized water, resulting in a total volume of 50.0 mL.
- Since the diluted solution was made by diluting 4.00 mL of stock solution, the concentration of Cu(II) in the diluted solution can be calculated by multiplying the stock concentration by the dilution factor: 0.201 M × (4.00 mL / 50.0 mL) = 0.0161 M.
3. Calculate the absorbance of the solution using Beer-Lambert's Law:
- Beer-Lambert's Law states that absorbance (A) is equal to the molar absorptivity (ε) multiplied by the path length (l) and the concentration (c): A = εcl.
- In this case, we know that the absorbance is 0.1776 and the path length is 1 cm.
- Rearranging the formula, we get: ε = A / (cl).
- Plug in the values: ε = 0.1776 / (0.0161 M × 1 cm) = 11.003 M^-1cm^-1.
4. Calculate the transmittance of the solution:
- Transmittance (T) is the ratio of the intensity of light transmitted through the solution to the intensity of the incident light, expressed as a percentage.
- Transmittance is calculated using the formula: T = 10^(-A).
- Plug in the value of absorbance obtained earlier: T = 10^(-0.1776) = 0.680.
Therefore, the transmittance of the solution is 0.680, or 68.0% when expressed as a percentage.