Muscle physiologists study the accumulation of lactic acid [CH3CH(OH)COOH] during exercise. Food chemists study its occurrence in sour milk, beer, wine, and fruit. Industrial microbiologists study its formation by various bacterial species from carbohydrates. A biochemist prepares a lactic acid-lacte buffer by mixing 225 mL of 0.85 M lactic acid (Ka = $1.38 \times 10 - 4$) with 435 mL of 0.68 M sodium lactate. What is the buffer pH?

What is the component concentration ratio. [NO2-]/[HNO2], of a buffer that has a pH of 2.95 (Ka of HNO2 = 7.1 $\times$10-4)?

Many drugs decompose in blood by a first-order process.
(e) Calculate $E_a$ for decomposition of the antibiotic in part (d).

A 35.00-mL solution of 0.2500 M HF is titrated with a standardized 0.1532 M solution of NaOH at $25 ^ { \circ } \mathrm { C }.$

What is the pH of the HF solution before titrant is added?

How many milliliters of titrant are required to reach the equivalence point?

What is the pH at 0.50 mL before the equivalence point?

A study was conducted of a diagnostic test (the FAIR test, i.e., hip flexion, adduction, and internal rotation) used to identify people with piriformis syndrome (PS), a pelvic condition that involves malfunction of the piriformis muscle (a deep buttock muscle), which often causes lumbar and buttock pain with sciatica (pain radiating down the leg). The FAIR test is based on nerve-conduction velocity and is expressed as a difference score (nerve-conduction velocity in an aggravating posture minus nerve-conduction velocity in a neutral posture). It is felt that the larger the FAIR test score, the more likely a participant will be to have PS. Data are given in the Data Set PIRIFORM.DAT for 142 participants without $\mathrm{PS}$ (piriform = 1) and 489 participants with PS (piriform = 2) for whom the diagnosis of $\mathrm{PS}$ was based on clinical criteria. The FAIR test value is called MAXCHG and is in milliseconds (ms). A cutoff point of $\geq 1.86 \mathrm{~ms}$ on the FAIR test is proposed to define a positive test.

The criterion of $\geq 1.86 \mathrm{~ms}$ to define a positive test is arbitrary. Using different cutoff points to define positivity, obtain the ROC curve for the FAIR test. What is the area under the ROC curve? What does it mean in this context?

Find a ratio equivalent to each ratio. Then use the ratios to write a proportion.

$$\frac{12}{25}$$

Human blood contains one buffer system based on phosphate species and one on carbonate species. Assuming that blood has a normal pH of 7.4, what are the principal phosphate and carbonate species present? What is the ratio of the two phosphate species? (In the presence of the dissolved ions and other species in blood, Ka1 of H3PO4 $= 1.3 \times 10 - 2$ Ka2 = $2.3 \times 10 - 7$ and Ka3 = $6 \times 10 - 12$; Ka1 of H2CO3 = $8 \times 10 - 7$ and Ka2 = $1.6 \times 10 - 10 . )$

Which element has three electrons in its 3d sublevel?

An axial-flow blower delivers

$$40 ft^3/s$$

of air that enters at 20°C and 1 atm. The flow passage has a 10-in outer radius and an 8-in inner radius. Blade angles are

$$\alpha_1 = 60°$$

and

$$\beta_2 = 70°$$

, and the rotor runs at 1800 r/min. For the first stage compute (a) the head rise and (b) the power required.

$\rule{1cm}{1pt}$ and $\rule{1cm}{1pt}$ drugs are used to relieve anxiety and tension without inducing sleep.

The system described in is to be designed using the frequency response techniques. Select the coefficients of $G_c(s)$ so that the phase margin is P.M. $=45^{\circ}$. Obtain the step response of the system with and without a prefilter $G_p(s)$.

In a poll conducted by the Pew Research Center in a certain year, 2000 adults ages 18 years old and older were asked how frequently they are in touch with their parents by phone. The results of the poll are as follows:

If a person who participated in the poll is selected at random, what is the probability that the person said he or she kept in touch with his or her parents:

a. Once a week?

b. At least once a week?

MBank hired El Paso Recovery Services to repossess the Pontiac Trans-Am owned by Sanchez because she was late on her loan payments. The repossessor went to Sanchez’s home with a tow truck and tried to hook the car to the tow truck. Sanchez, who was cutting her grass at the time, asked what they were doing. The repossessors didn’t respond. Sanchez then locked herself in the car to try to stall them until the police arrived. The repossessor finally towed the Trans Am on a high-speed trip, with Sanchez inside, to a repossession lot where they left the car in a fenced and locked yard. Police later rescued Sanchez. She sued MBank. Will she recover? (MBank of El Paso v. Sanchez, 836 S.W.2d 151, Tex.)

Solve the area of the shaded region.