What is Le Ch$\^{a}$telier's principle? Consider the reaction $2 \mathrm{NOCl}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+$ $\mathrm{Cl}_2(\mathrm{~g})$. If this reaction is at equilibrium, what happens when the following changes occur?

For this change, what happens to the value of $K$ for the reaction as equilibrium is reached again? Give an example of a reaction for which the addition or removal of one of the reactants or products has no effect on the equilibrium position.

$\mathrm{NOCl}(\mathrm{g})$ is added.

In general, how will the equilibrium position of a gas-phase reaction be affected if the volume of the reaction vessel changes? Are there reactions that will not have their equilibria shifted by a change in volume? Explain. Why does changing the pressure in a rigid container by adding an inert gas not shift the equilibrium position for a gas-phase reaction?

Why must the absolute value of the common ratio be less than 1 before an infinite geometric sequence can have a sum?

In Exercises, use the graph of $f^{\prime}$ to sketch a graph of $f$ and the graph of $f^{\prime \prime}$.

Using the previous problem, describe the type of function represented.

Solve the percent problem. 1.8 is 72% of what number?

Complete the following sentence using the imperfect form of the verb in parentheses. Follow the model.

Modelo Nosotros (ir) íbamos_______ a la escuela todos los días.

¡Mi mamá (ser)_______ muy traviesa de niña!

Read this passage. Then answer the questions below it.

I soon found out why old Chong had retired from teaching piano. He was deaf. "Like Beethoven!" he shouted to me.

What are the personal pronouns in this sentence?

What is Le Ch$\^{a}$telier's principle? Consider the reaction $2 \mathrm{NOCl}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+$ $\mathrm{Cl}_2(\mathrm{~g})$. If this reaction is at equilibrium, what happens when the following changes occur?

For this change, what happens to the value of $K$ for the reaction as equilibrium is reached again? Give an example of a reaction for which the addition or removal of one of the reactants or products has no effect on the equilibrium position.

$\mathrm{Cl}_2(g)$ is removed.

In general, how will the equilibrium position of a gas-phase reaction be affected if the volume of the reaction vessel changes? Are there reactions that will not have their equilibria shifted by a change in volume? Explain. Why does changing the pressure in a rigid container by adding an inert gas not shift the equilibrium position for a gas-phase reaction?

If $f(x)=\left(x^2-1\right) e^x$, find $f^{\prime}(x)$ and $f^{\prime \prime}(x)$.

Repeat previous problem, using calculus to handle the triangular portion.

Y.C. was in labor for 12 hours and gave birth vaginally to Baby H, her first child. The nurse will complete the physical assessment and observe for physiologic changes in the newborn's transition from intrauterine to extrauterine life.

Y.C. has decided to breastfeed her infant. She asks for assistance. Identify 6 important points to include in your teaching plan.

Find the indicated term of the following arithmetic sequence.

$-8,-6,-4,-2, \ldots, 100^{\text {th }}$ term

$$y=x^2$$

Indicate what kind of curve is represented by above equation and find its curvature, using $\kappa(t)=\frac{\sqrt{\left(\mathbf{r}^{\prime} \cdot \mathbf{r}^{\prime}\right)\left(\mathbf{r}^{\prime \prime} \cdot \mathbf{r}^{\prime \prime}\right)-\left(\mathbf{r}^{\prime} \cdot \mathbf{r}^{\prime \prime}\right)^2}}{\left(\mathbf{r}^{\prime} \cdot \mathbf{r}^{\prime}\right)^{3 / 2}} .$ or $\kappa(x)=\frac{\left|y^{\prime \prime}\right|}{\left(1+y^{\prime 2}\right)^{3 / 2}} \quad\quad\quad\left(y^{\prime}=\frac{d y}{d x}, \text { etc. }\right)$

Another D-2-ketohexose, psicose, yields a mixture of allitol and altritol when reduced with ${NaBH}_4$ (see Problem 44). Determine the structure of psicose.

Problem 44:

One of the D-2-ketohexoses (see the previous problem) is called sorbose. On treatment with ${NaBH}_4$, sorbose yields a mixture of gulitol and iditol. What is the structure of D-sorbose? (Gulitol and iditol are the alditols acquired by reduction of gulose and idose.)

Previous problem:

How many D-2-ketohexoses are there? Sketch them.