As NaCl(s) dissolves according to the equation NaCl(s) $\rightarrow$ Na+(aq) + $\mathrm{Cl}_{2}(a q)$, the entropy of the system (1) decreases (2) increases (3) remains the same

Which change in a sample of water is accompanied by the greatest increase in entropy? (1) $\mathrm{H}_{2} \mathrm{O}(\mathrm{\ell})$ at $100^{\circ} C$ is changed to $\mathrm{H}_{2} \mathrm{O}(g)$ at $200^{\circ} C$ (2) $\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ at $100^{\circ} C$ is changed to $\mathrm{H}_{2} \mathrm{O}(g)$ at $200^{\circ} C$ (3) $\mathrm{H}_{2} \mathrm{O}(\mathrm{s})$ at $-100^{\circ} C$ is changed to $\mathrm{H}_{2} \mathrm{O}(s)$ at $0^{\circ} C$ (4) $\mathrm{H}_{2} \mathrm{O}(\mathrm{s})$ at $0^{\circ} C$ is changed to $\mathrm{H}_{2} \mathrm{O}(\ell)$ at $0^{\circ} C$.

Which tendencies favor a spontaneous reaction? (1) lower energy and decreasing entropy (2) lower energy and increasing entropy (3) higher energy and decreasing entropy (4) higher energy and increasing entropy

Write a chemical equation for the dissociation of NaCl, AlCl$_3$, and CaCl$_2$ in water.

If f(x) has a positive slope everywhere, and g(x) has a negative slope everywhere, decide if h(x) is increasing, or decreasing, or neither. h(x) = f(f(x))

Write the dissociation reaction of NaCl in water.

As a brown bear with a radio collar walks along a river, the distance from the bear to an observation post after t seconds is given by the function

$$d ( t ) = \sqrt { 1600 + 9 t ^ { 2 } }$$

Find and interpret the inverse of d(t).

Consider the formula

$$(n)_k=\frac{n}{(n-k)!}$$

This formula is mostly correct. For what values of n and k is it correct? Prove the formula is correct under a suitable hypothesis; that is, this problem asks you to find and prove a theorem of the form "If (conditions on n and k), then $(n)_k$=n!/(n-k)!."

The hydrocarbon octane $\left( C _8 H _{18}\right)$ burns to give $CO _2$ and water vapor:

$$\begin{align*} 2 C _8 H _{18}( g )+25 O _2( g ) \rightarrow 16 CO _2( g )+18 H _2 O ( g ) \end{align*}$$

If a 0.048-g sample of octane burns completely in $O _2$, what will be the pressure of water vapor in a $4.75$-L flask at $30.0^{\circ} C$? If the $O _2$ gas needed for complete combustion was contained in a $4.75$ - L flask at $22^{\circ} C$, what would its pressure be?

Write balanced molecular and net ionic equations for the reactions of manganese with dilute sulfuric acid.

Does the entropy of the system increase or decrease for each of the following? Explain.
c. dissolving $\mathrm{NaCl}$ in water

The recent Democratic and Republican presidential state primary elections were highlighted by the difference in the way winning candidates were awarded delegates. In Republican states, the winner is awarded all the state’s delegates; conversely, the Democratic state winner is awarded delegates in proportion to the percentage of votes. This led to a Chance (Fall 2007) article on making your vote count. Consider a scenario where you are one of five county commissioners voting on an issue, where each commissioner is equally likely to vote for or against.
Your vote counts (i.e., is the decisive vote) only if the other four voters split, 2 in favor and 2 against. Use the binomial distribution to find the probability that your vote counts.

write the complex number in standard form. (3 + √-5)(7 - √-10)

In what ways might limited life be considered an advantage for sole proprietors?