Standard Deviation

In an attempt to determine the gas flow rate produced

from an aquarium pump inexpensively, students devised a

simple laboratory scheme that included a water-filled

bucket, a 2 L graduated cylinder and a stop watch. As

shown in Figure 1.8, the air from the pump was collected

into an inverted, water-filled graduated cylinder whose

opening was held under the water surface in a bucket.

Error Propagation

Consider the experiment outlined in Example 1.2. The

uncertainty of the experimental time was assumed to be

1 second (1/60 min). Use the rules for error propagation to

determine the uncertainty in Q, 

Error Propagation

A wide variety of manufacturers, including the textile,

food, paper and cosmetic industries, utilize azo dyes in

their production processes. As a result, color-laden

industrial wastewater is frequently discharged into the

environment and produces an obnoxious appearance that

is not favorably perceived by regulators or the public. In

general, azo dyes are not considered hazardous, but are

often considered recalcitrant in traditional wastewater

treatment processes. In the United States, color is

federally regulated by a secondary maximum

contaminant level under the Drinking Water Act (40 CFR

143.2), while some states mandate an additional level of

compliance.

  As a result of regulatory and public relation problems,

industries discharging color have recently begun focusing

on novel decolorization processes such as ozonation,

catalytic oxidation, adsorption, and hybrid technologies

that combine ozonation with biological treatment

schemes. Acid yellow 17 dye (C16H12Cl2N4O7S2⋅2Na;

MW = 551.29) is a common additive found in ordinary

household products such as shampoo, bubble bath, shower

gel, liquid soap, multipurpose cleanser, dishwashing liquid

and alcohol-based perfumes. As regulations associated

with dyestuff are tightened, associated industries are faced

with finding economically viable water treatment

solutions.

During laboratory experiments with dye-laden

wastewater, the concentration of dye required routine

measurement. A calibration curve that related absorbance

to concentration was used. The dye concentration was

measured, using a device called a spectrophotometer, at a

wavelength of 400 nm, and a standard curve was prepared,

showing the absorbance versus concentration of acid

yellow 17 dye. From the calibration curve, the

concentration of the dye in the wastewater sample was

found to be 250 ± 5 mg/L. The solution was prepared by

dissolving 0.0625 g of the dye into 250.0 ± 0.5 mL of water.

Find the uncertainty of the dye weight that was actually

added to make the stock solution.

Least-squares Linear  Regression

Many wastewater treatment plants use microbiological

processes to degrade the organic contaminants commonly

associated with municipal wastewater. Two measurements

often used by municipalities and regulators to characterize

the organic content in the wastewater include the

biochemical oxygen demand (BOD) and the chemical

oxygen demand (COD) parameters. The BOD5

measurement quantifies how much oxygen the aerobic

microbes within the treatment system require to oxidize

the degradable organics in the water during a five-day

reaction period. The COD measures the amount of oxygen

required to oxidize chemically all of the organic material in

the wastewater. A more detailed description of these two

important parameters will be covered in Chapter 3. At this

juncture, you should observe the correlations between

these parameters in this example problem].

Given the data in Table 1.7 to describe the relationship

between the influent COD and BOD5 for the wastewater

treatment plant; use the data to calculate means, standard

deviations for BOD5 and COD, correlation r, coefficient of

determination R2, slope m, intercept b, and the equation of

the least-squares line for this case.

Linear Manipulation of  Non-linear Models

A semi-batch bubble column was used to test the affect of

ozone on a synthetically prepared wastewater that

contained acid yellow 17 dye. The carrier gas flow rate was

maintained at a constant flow, resulting in uniform ozone

introduction to the system. The gas feed was sparged

through three stainless steel filters that entered the side of

the reactor near the bottom of the column. Figure 1.13

provides a schematic of the laboratory test equipment.

Color concentration was measured spectrophotometrically

using a Spectronic 20D+ at a wavelength of 400 nm.

Experimental results showing the removal of color

from the wastewater are shown in the table below.

Using the data provided and the equation shown

below (assume the data are well modeled using first order

kinetics), find the first-order rate constant, k, which

characterizes the decolorization of the wastewater, and

estimate the initial dye concentration.

where:

Ct = is the dye concentration at some time, t

C0 = represents the initial dye concentration

k = is the first-order rate constant.