Tris(hydroxymethyl) aminomethane, known as TRIS or THAM, is a water-soluble base used to synthesize surfactants and pharmaceuticals, as an emulsifying agent in cosmetics, and in cleaning mixtures for textiles and leather. In biomedical research, solutions of TRIS are used to maintain nearly constant pH for the study of enzymes and other cellular components. Given that the pKb is 5.91, calculate the pH of 0.075 M TRIS.

Consider the formation of a dimeric protein

$$2 \mathrm{P} \longrightarrow \mathrm{P}_2$$

At $25^{\circ} \mathrm{C}$, we have $\Delta H^{\circ}=17 \mathrm{~kJ} / \mathrm{mol}$ and $\Delta S^{\circ}=65 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}$. Is the dimerization favored at this temperature? Comment on the effect of lowering the temperature. Does your result explain why some enzymes lose their activities under cold conditions?

Calculate the electric field due to a uniformly charged rod of length $L$, aligned with the $x$-axis with one end at the origin; at a point $P$ on the $z$-axis.

You have three resistors, each of which has a resistance R. By connecting all three together in various ways, which one or more of the following resistance values can you obtain? (a) 3R, (b) $\frac{3}{2}$R, (c) R, (d) $\frac{2}{3}$R, (e) $\frac{1}{3}$R.

"Tris" is short for tris(hydroxymethyl) aminomethane. This weak base is widely used in biochemical research for the preparation of buffers. It offers low toxicity and a pKb (5.92 at 25°C) that is convenient for the control of pH in clinical applications. A buffer is prepared by mixing 0.050 mol of tris with 0.025 mo! of HCl in a volume of 2.00 L. Compute the pH of the solution.

Use a straightedge to draw a triangle. Construct the perpendicular bisector of each side of the triangle, and extend the bisectors into the interior of the triangle. Mark the point of intersection of the three bisectors. This is the circumcenter of the triangle. Use your compass to compare the distance from the circumcenter to each vertex of the triangle. What is remarkable about the distances?

Find $f^{\prime}(x)$ and find the equation of the line tangent to the graph of fat x=2. $f(x)=\frac{2 x-5}{2 x-3}$

A neurologist is investigating a deficiency in her patient's levels of the neurotransmitter, serotonin. Which of the following processes should she spend the most time analyzing?

a. The amount of serotonin broken down by enzymes

b. The amount of serotonin recycled during reuptake

c. The amount of serotonin created during reuptake

d. The amount of serotonin needed to fill the synapse

David no se siente bien y va la oficina de la enfermera de la escuela. Complete este diálogo con las formas apropiadas de estar.

DAVID: No lo creo. Él debe _________ en la oficina de uno de sus clientes.

A perpendicular cut through a water pipe reveals a circular cross section. The diameter of a

$$\frac { 3 } { 4 } - \text { inch }$$

pipe is 50% greater than the diameter of a

$$\frac { 1 } { 2 } \text { -inch }$$

pipe. The cross-sectional area of the larger pipe is what percent greater than the cross-sectional area of the smaller pipe?

You are at camp with a friend who is allergic to peanuts. How can you help determine which foods are safe for him to eat?

A contaminant is leaking into a lake at a rate of $R(t)=1600 e^{0.06 t} gal / h$. Enzymes that neutralize the contaminant have been added to the lake over time so that after $t$ hours the fraction of contaminant that remains is $S(t)=e^{-0.32 t}$. If there are currently 10,000 gallons of the contaminant in the lake, how many gallons will be present in the lake 18 hours from now?

When an apple is cut open, the inside soon turns brown. This is because enzymes that are released from the cut cells react with certain molecules in the apple. Rubbing lemon juice (which contains citric acid) on the cut apple prevents it from browning. Explain why this is so.

A 5.60-kg bucket of water is accelerated upward by a cord of negligible mass whose breaking strength is 75.0 N. If the bucket starts from rest, what is the minimum time required to raise the bucket a vertical distance of 12.0 m without breaking the cord?