A 0.200 g sample containing Cu is dissolved, and a diethyldithiocarbamate
coloured complex is formed. The solution is then diluted to 50.0 mL and the
absorbance measured as 0.260. A 0.500 g sample containing 0.240% Cu is
treated in the same manner, and the resulting solution has an absorbance of
0.600. Calculate the percentage of Cu in the sample. What is the molar
absorptivity of the Cu complex formed?
The easy way to do this is to work in g and A units. You know 0.5g sample x 0.240E-2 = 1.2E-3 g Cu. You know the ratio of A unit is 0.250 vs 0.6; therefore, 1.2E-3 g Cu x (.260/0.6) = ? g Cu in the unknown.
To calculate molar absorptivity use
A = ebc. Technically I don't think you can calculate this since the cell length is not given. However, in most cases this is 1 cm so
A = 0.6
b = 1 and c is calculated as follows:
(0.5g x 0.24E-2 x (1 mol/63.55) = mols Cu and convert to M by mols/L (L is 0.050 from dissolving in 50 ml). Then substitute and solve for e.
Oh boy, you've got quite the chemistry question there! But don't worry, Clown Bot is here to help with a touch of humor.
To calculate the percentage of Cu in the sample, you'll need to use some good old-fashioned math.
Let's start with the first sample. We know that the initial mass is 0.200 g and the absorbance is 0.260. Since we diluted the solution to 50.0 mL, we can use these numbers to determine the concentration of the Cu complex in the solution.
Now, for the second sample, we have a mass of 0.500 g and an absorbance of 0.600. Again, using the dilution factor of 50.0 mL, we can figure out the concentration of the Cu complex in this solution.
Next, we need to find the molar absorptivity of the Cu complex. This can be calculated by dividing the absorbance of each sample by its respective concentration of the Cu complex.
With these calculations, you can find the percentage of Cu in the sample and the molar absorptivity of the Cu complex. Happy number crunching!
To calculate the percentage of Cu in the sample, we can use the Beer-Lambert Law and compare the absorbance values.
Step 1: Calculate the concentration of Cu in the first sample.
Given:
Sample mass = 0.200 g
Absorbance = 0.260
Dilution factor = V_final / V_initial = 50.0 mL / 1.0 mL = 50
The formula for the Beer-Lambert Law is A = εbc, where A is the absorbance, ε is the molar absorptivity, b is the path length, and c is the concentration.
We can rearrange this formula to solve for concentration: c = A / (εb).
In this case, we know the absorbance (A), the dilution factor (b), and path length (1 cm). We need to find the molar absorptivity (ε) to calculate the concentration.
Step 2: Calculate the concentration of Cu in the second sample.
Given:
Sample mass = 0.500 g
Cu percentage = 0.240%
Absorbance = 0.600
Dilution factor = V_final / V_initial = 50.0 mL / 1.0 mL = 50
To calculate the concentration of Cu, we need to convert the Cu percentage to a decimal.
Cu percentage = (mass of Cu / sample mass) * 100
0.240% = (mass of Cu / 0.500 g) * 100
Rearranging the equation:
mass of Cu = (0.240% / 100) * 0.500 g = 0.0012 g
Now we can calculate the concentration of Cu in the second sample using the mass of Cu, absorbance, dilution factor, and path length.
Step 3: Calculate the percentage of Cu in the sample.
To calculate the percentage of Cu in the second sample, we can use the formula:
Cu percentage = (mass of Cu / sample mass) * 100
Let's calculate the values:
For the first sample:
Concentration of Cu = A / (εb) = 0.260 / (ε * 1.0) g/L
Concentration in mg/L = 0.260 * 1000 mg
Concentration in g/L = (0.260 * 1000 mg) / 1000 g
For the second sample:
Concentration of Cu = A / (εb) = 0.600 / (ε * 1.0) g/L
Concentration in mg/L = 0.600 * 1000 mg
Concentration in g/L = (0.600 * 1000 mg) / 1000 g
Now we can equate the concentrations of both samples:
(0.260 * 1000 mg) / 1000 g = (0.600 * 1000 mg) / 1000 g
Solving for mg:
0.260 * 1000 mg = 260 mg
0.600 * 1000 mg = 600 mg
Now we can calculate the percentage of Cu in the second sample:
Cu percentage = (mass of Cu / sample mass) * 100 = (0.0012 g / 0.500 g) * 100
Finally, we can calculate the molar absorptivity (ε) using the concentration of Cu in the second sample, absorbance, dilution factor, and path length:
ε = A / (c * b) = 0.600 / (c * 1.0)
Now you can plug in the values and calculate the percentage of Cu in the sample and the molar absorptivity of the Cu complex formed.
To calculate the percentage of Cu in the sample, we need to use the absorbance measurements and the information provided.
Let's deduce the steps to calculate the percentage of Cu in the sample:
1. For the first sample:
- Mass of the sample = 0.200 g
- Absorbance = 0.260
- Volume of the solution = 50.0 mL
2. For the second sample:
- Mass of the sample = 0.500 g
- Absorbance = 0.600
- Volume of the solution = 50.0 mL
Now, we can calculate the molar absorptivity of the Cu complex:
1. Make sure the volumes for both samples are the same since they were both diluted to 50.0 mL.
2. Use the Beer-Lambert Law to calculate the molar absorptivity (ε).
The Beer-Lambert Law is given by the equation: A = εcl
Where:
- A is the absorbance
- ε is the molar absorptivity
- c is the concentration of the solution in mol/L
- l is the path length of the cuvette in cm (usually 1 cm)
Since the volumes are the same for both samples, the concentrations will be directly proportional to the mass percentages of Cu in each sample.
Let's calculate the percentage of Cu in each sample:
1. For the first sample:
- Percentage of Cu = (mass of Cu / mass of sample) x 100
mass of Cu = 0.240% of 0.200 g
= (0.240 / 100) x 0.200 g
- Percentage of Cu in the first sample = [(0.240 / 100) x 0.200 / 0.200] x 100
2. For the second sample, we already have the mass percentage of Cu, which is 0.240%.
Now, we can calculate the molar absorptivity of the Cu complex using the Beer-Lambert Law equation:
1. For the first sample:
- A = 0.260
- c = (percentage of Cu in the first sample) / (molar mass of Cu)
- l = 1 cm (assumed)
Substitute the values in the equation: A = εcl and solve for ε.
2. For the second sample:
- A = 0.600
- c = (percentage of Cu in the second sample) / (molar mass of Cu)
- l = 1 cm (assumed)
Substitute the values in the equation: A = εcl and solve for ε.
Finally, with the percentage of Cu in the sample and the molar absorptivity of the Cu complex, you will have the answers to all the questions.