Predict the ground-state electron configurations of $\mathrm{Al}$. Ga, and In.

Write electron configurations for the following elements. (a) C (b) P (c) Cl (d) K

A first-order reaction $\mathrm{A} \longrightarrow$ products have a half-life of $13.9 \mathrm{~min}$. The rate at which this reaction proceeds when $[\mathrm{A}]=0.40 \mathrm{M}$ is
(a) $0.020 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~min}^{-1}$;
(b) $5.0 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~min}^{-1}$;
(c) $8.0 \mathrm{~mol} \mathrm{~L}-1 \mathrm{~min}^{-1}$
(d) $0.125 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~min}^{-1}$.

In given problem, find all values of c that satisfy the Mean Value Theorem for Integrals on the given interval.

$$q(y)=a y^2 ; \quad[0, b]$$

Write electron configurations for the following atoms and ions, and comment on the result. Cl$^-$

Imagine that on a cold day you are planning to take a thermos of hot soup with you on a hike. Explain why you might fill the thermos with hot water first before filling it with the hot soup.

How could you measure the acceleration of a spaceship by using only simple instruments (such as springs, strings, and rulers) located within the ship?

The cart has a mass of $m$ and is attached to two springs, each having a stiffness of $k_1-k_2-k$, unstretched length of $I_0$, and a stretched length of $l$ when the cart is in the equilibrium position. If the cart is displaced a distance of $x=x_0$ such that both springs remain in tension $\left(x_0<l-l_0\right)$, determine the natural frequency of oscillation.

Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that was accelerating upward? That was accelerating downward?

Look at the electron configurations in Figure 2.17, and identify the 21 anomalous ones.

Factor. If a polynomial is prime, state this.

$$56 x+x^2-x^3$$

What are the R,S configurations of the three chirality centers in D-xylose?

What are the symbols for the elements with the following valence electron configurations? $s^2 p^6$

(a) If $u(x, y)=f(x y)$, prove that u satisfies the partial differential equation $x \frac{\partial u}{\partial x}-y \frac{\partial u}{\partial y} = 0$. Find a solution such that $u(x, x)=x^{4} e^{x^{2}}$ for all x. (b) If $v(x, y)=f(x / y)$ for $y \neq 0$, prove that v satisfies the partial-differential equation $x \frac{\partial v}{\partial x}+y \frac{\partial v}{\partial y}=0$. Find a solution such that $v(1,1)=2$ and $D_{1} v(x, 1 / \mathrm{x})=1 / \mathrm{x}$ for all $\mathrm{x} \neq 0$