The rate constant for the second-order reaction

$$2 \mathrm{NOBr}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_2(\mathrm{~g})$$

is $0.80 \mathrm{M}^{-1} \mathrm{~s}^{-1}$ at $10^{\circ} \mathrm{C}$.
Starting with a concentration of $0.086 \mathrm{M}$, calculate the concentration of $\mathrm{NOBr}$ after 22 s.

Compound A diffuses through a 4-cm-long tube and reacts as it diffuses. The equation governing diffusion with reaction is

$$D \frac { d ^ { 2 } A } { d x ^ { 2 } } - k A = 0$$

At one end of the tube, there is a large source of A at a concentration of 0.1 M. At the other end of the tube there is an adsorbent material that quickly absorbs any A, making the concentration 0 M.

$$\text { If } D = 1.5 \times 10 ^ { - 6 } \mathrm { cm } ^ { 2 } / \mathrm { s } \text { and } k = 5 \times 10 ^ { - 6 } \mathrm { s } ^ { - 1 },$$

what is the concentration of A as a function of distance in the tube?

The concentration C in(mg/ml) milligrams per milliliter (mg/ml) of a certain drug in a person’s bloodstream t hrs after a pill is swallowed is modeled by

$$C(t)=1+\frac{4 t}{1+t^{3}}-e^{-0.06 t}.$$

Estimate the change in concentration when t changes from 20 to 30 min.

Chemotaxis is the phenomenon in which organisms move toward or away from certain chemicals. Suppose that a bacterium finds food by always moving toward the highest concentration of glucose. If it starts at the point (1, 2) in the xy-plane and the concentration of glucose, in certain units, is $f(x, y)=\frac{1}{1+x^{2}+y^{2}}$ find the direction in which the bacterium will move initially.

In a titration, a few drops of an indicator are added to a flask containing 35.0 milliliters of $\mathrm{HNO}_{3}(a q)$ of unknown concentration. After 30.0 milliliters of 0.15 M NaOH(aq) solution is slowly added to the flask, the indicator changes color, showing the acid is neutralized. Show a correct numerical setup for calculating the concentration of the $\mathrm{HNO}_{3}(a q)$ solution.

$$\mathrm{N}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftarrows 2 \mathrm{NO} \quad K=4.1 \times 10^{-4}$$

If the reaction began with $0.100 \mathrm{molL}^{-1}$ of $\mathrm{N}_2$ and $0.100 \mathrm{molL}^{-1}$ of $\mathrm{O}_2$, what were the equilibrium concentrations of all species?

In the above another trial was carried out. The reaction began with an initial concentration of $\mathbf{N}_2$ equal to the initial concentration of NO. Each had a concentration of $0.100 \mathrm{molL}^{-1}$. What were the equilibrium concentrations of all species?

A patient is injected with a drug, and t hours later, the concentration of the drug remaining in the patient's bloodstream is given by $C(t)=\frac{3 t}{\left(t^{2}+36\right)^{3 / 2}} \quad \mathrm{mg} / \mathrm{cm}^{3}.$ What is the average concentration of drug during the first 8 hours after the injection?

Regulation of PFK$-1$ The effect of ATP on the allosteric enzyme PFK$-1$ is shown below. For a given concentration of fructose $6-$phosphate, the PFK$-1$ activity increases with increasing concentrations of ATP, but a point is reached beyond which increasing the concentration of ATP inhibits the enzyme.
(a) Explain how ATP can be both a substrate and an inhibitor of PFK-1. How is the enzyme regulated by ATP?
(b) In what ways is glycolysis regulated by ATP levels?
(c) The inhibition of PFK-1 by ATP is diminished when the ADP concentration is high, as shown in the graph. How can this observation be explained?

The solubility product of $\mathrm{Mg}(\mathrm{OH})_2$ is $1.2 \times 10^{-11}$.

What minimum $\mathrm{OH}^{-}$concentration must be attained (e.g., by adding $\mathrm{NaOH}$ ) to decrease the $\mathrm{Mg}$ concentration in a solution of $\mathrm{Mg}\left(\mathrm{NO}_3\right)_2$ to less than $1.0 \times 10^{-10} \mathrm{M}$ ?

Use the following information. The pH of a person's blood is given by $\mathrm{pH}=6.1+\log _{10} B-\log _{10} C$, where $B$ is the concentration of bicarbonate, which is a base, in the blood and $C$ is the concentration of carbonic acid in the blood. Most people have a blood $\mathrm{pH}$ of 7.4. What is the approximate ratio of bicarbonate to carbonic acid for blood with this pH?

Water at $374^{\circ} \mathrm{C}$ and 218 atmospheres of pressure transforms into what is called a supercritical fluid, which behaves both as a liquid and as a gas. In a neutral solution of supercritical water the $\mathrm{pH}$ is about $2$ . What is the concentration of hydronium ions in this neutral solution? What is the concentration of hydroxide ions? Why is supercritical water so corrosive?

A patient is injected with a drug, and $t$ hours later, the concentration of the drug remaining in the patient's bloodstream is given by

$$C(t)=\frac{0.3 t}{\left(t^2+16\right)^{1 / 2}} \quad \mathrm{mg} / \mathrm{cm}^3$$

What is the average concentration of the drug during the first 3 hours after the injection?

(a) What volume is a serving of orange juice?

(b) How many servings in $1 \mathrm{~L}(1000 \mathrm{~mL})$ of orange juice?

(c) What is the concentration of potassium in $\mathrm{g} / \mathrm{L}(1 \mathrm{~g}=1000 \mathrm{mg})$ ?

(d) What is the concentration of sugars per liter in $\mathrm{g} / \mathrm{L}$ ?

Salt concentration Salt water of concentration $0.1$ pound of salt per gallon flows into a large tank that initially contains $50$ gallons of pure water.

If the flow rate of salt water into the tank is $5 \mathrm{gal} / \mathrm{min}$, find the volume $V(t)$ of water and the amount $A(t)$ of salt in the tank after $t$ minutes.