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Assume a sewage treatment plant processing 1 million liters of wastewater per da...
May 13, 2024
Assume a sewage treatment plant processing 1 million liters of wastewater per day
containing 200 mg/L of degradable biomass, CH2O. Calculate the minimum
volume of dry air at 25 degree that must be pumped into the wastewater per day to
provide the oxygen required to degrade the biomass.
Solution
1
Calculate the mass of degradable biomass: First, we need to calculate the total mass of degradable biomass (CH2O) in the wastewater
The mass of biomass can be calculated using the concentration and the volume of wastewater. The formula is: mass (mg) = concentration (mg/L) × volume (L).
2
Determine the stoichiometry of the reaction: The balanced chemical equation for the degradation of CH2O with oxygen (O2) is: CH2O+O2→CO2+H2O. From the equation, 1 mole of CH2O requires 1 mole of O2 for complete degradation
3
Calculate the moles of O2 required: To find the moles of O2 needed, we convert the mass of CH2O to moles and use the stoichiometry from the balanced equation. The molar mass of CH2O is 30.026 g/mol
4
Convert moles of O2 to volume of dry air: Dry air is approximately 21% oxygen by volume. To find the volume of dry air needed, we calculate the volume of O2 and then account for the fact that only 21% of air is O2. The ideal gas law (PV=nRT) will be used, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin
5
Perform the calculations: Using the steps above, we will perform the calculations to find the minimum volume of dry air required
Answer
[Insert final answer here]
Key Concept
Stoichiometry and gas laws are essential for calculating the volume of air required to provide oxygen for the degradation of biomass in wastewater.
Explanation
The calculation involves determining the mass of biomass, converting it to moles, using the stoichiometry of the reaction to find the moles of oxygen needed, and then using the ideal gas law to find the volume of dry air at the given conditions
10 mL aliquots of a natural water sample were pipetted into 50 mL volumetric
flasks. Exactly 0, 5, 10, 15 and 20mL of a standard solution containing 11.1ppm
of Fe
3+ were added to each flask, followed by an excess of thiocynate ion to give
the red complex Fe(SCN)
2+
. After dilution to volume, the instrument response for
each of the five solutions, measured with a colorimeter, was found to be 0.240, 0.437, 0.621, 0.809 and 1.009 respectively. Determine the original concentration
of Fe
3+
in the water sample. (2 points)
Solution
1
Create a calibration curve: Use the instrument response values for the known concentrations of the standard solution to create a calibration curve. The concentration of Fe3+ in ppm for the standard solutions are 0, 1.11, 2.22, 3.33, and 4.44 ppm, corresponding to the volumes of standard solution added
2
Plot the data and find the equation of the line: Plot the instrument response against the concentration of Fe3+ to obtain the best fit line. The equation of this line is typically in the form of y=mx+b, where y is the instrument response, m is the slope, x is the concentration of Fe3+, and b is the y-intercept
3
Determine the concentration of Fe$^{3+}$ in the sample: Use the instrument response for the sample (0.240) and the equation of the calibration curve to calculate the concentration of Fe3+ in the sample
Answer
[Insert final answer here]
Key Concept
Calibration curve in spectrophotometry
Explanation
A calibration curve is used to determine the concentration of a substance in a sample by comparing the instrument response of the sample to a series of known standards.
Air sampling was performed continuously for 1 hour every 4 hours and this was
repeated six times. The flow rate was set at 0.5L/min. At the end of sampling, the
absorption solution was diluted to 50mL and 20mL aliquot was taken out for
measurement of SO2 using spectrometry. The result was 6.0μg. The daily
average air temperature was 25 ºC and the air pressure was 95 KPa. Calculate the
daily average concentration of SO2 of this site under standard condition (0 ºC, 101.3 KPa) and expressed the result in both units of mg/m3 and ppm.
Solution
1
Calculate the total volume of air sampled: The air was sampled for 1 hour every 4 hours, repeated six times, with a flow rate of 0.5 L/min
$ \text{Total volume} = \text{Flow rate} \times \text{Sampling time per session} \times \text{Number of sessions} = 0.5 \, \text{L/min} \times 60 \, \text{min} \times 6 = 180 \, \text{L} $
2
Convert the mass of SO2 to standard conditions: Use the ideal gas law to convert the measured mass to standard conditions
$ \text{Mass under standard conditions} = \text{Measured mass} \times \frac{\text{Standard pressure}}{\text{Measured pressure}} \times \frac{\text{Measured temperature} + 273.15}{\text{Standard temperature} + 273.15} = 6.0 \, \mu\text{g} \times \frac{101.3 \, \text{kPa}}{95 \, \text{kPa}} \times \frac{25 + 273.15}{0 + 273.15} $
3
Calculate the concentration in mg/m³: Divide the mass of SO2 under standard conditions by the total volume of air sampled
$ \text{Concentration (mg/m³)} = \frac{\text{Mass under standard conditions (in mg)}}{\text{Total volume (in m³)}} $
4
Calculate the concentration in ppm: Use the conversion factor between mg/m³ and ppm for SO2 at standard conditions
$ \text{Concentration (ppm)} = \text{Concentration (mg/m³)} \times \frac{24.45}{\text{Molar mass of SO2}} = \text{Concentration (mg/m³)} \times \frac{24.45}{64.066 \, \text{g/mol}} $
Answer
[Insert final answer here after performing the calculations]
Key Concept
Calculating the concentration of a pollutant in air requires accounting for the volume of air sampled and converting the measured mass to standard conditions using the ideal gas law.
Explanation
The concentration of SO2 is determined by the mass of SO2 collected and the volume of air sampled. To compare with standard conditions, the mass is adjusted using the ideal gas law, and the concentration is then expressed in both mg/m³ and ppm.
There are three sources of noise whose levels are 70dB, 75dB and 65dB
respectively. Please calculate the total sound pressure level.
To calculate the total sound pressure level from multiple sources of noise, you can use the formula for combining sound levels in decibels.
First, you need to convert the individual sound levels from decibels to sound pressure levels in pascals. The formula to convert decibels to pascals is:
Sound Pressure Level (in pascals) = 20 * 10^(Sound Level in dB / 20)
Once you have the sound pressure levels in pascals for each source of noise, you can add them together and then convert the total back to decibels using the formula:
Total Sound Level (in dB) = 20 * log10(Total Sound Pressure Level / 20)
By following these steps for the noise levels of 70dB, 75dB, and 65dB, you can calculate the total sound pressure level. Let me know if you need further assistance with the calculations!
If the Earth is 5 billion years old, how much of the uranium-238 that was present
at the time of formation of the Earth still here today? (t½ for
238U = 4.51 x 10
9
years )(2 points
Solution
1
Calculate the number of half-lives: The number of half-lives that have passed can be calculated by dividing the age of the Earth by the half-life of uranium-238
$$ \text{Fraction remaining} = \left(\frac{1}{2}\right)^n $$
3
Perform the calculation: Substitute the value of n from step 1 into the equation from step 2 to find the fraction of uranium-238 that remains
$$ \text{Fraction remaining} \approx \left(\frac{1}{2}\right)^{1.1086} \approx 0.47 $$
Answer
Approximately 47% of the uranium-238 that was present at the time of formation of the Earth is still here today.
Key Concept
Half-life and exponential decay
Explanation
The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula (21)n, where n is the number of half-lives that have elapsed.
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