Explain the following seeming contradiction: You have two gases, A and B, in two separate containers of equal volume and at equal pressure and temperature. Therefore, you must have the same number of moles of each gas. Because the two temperatures are equal, the average kinetic energies of the two samples are equal. Therefore, since the energy of such a system corresponds to translational motion, the root mean square velocities of the two are equal, and thus the particles in each sample move, on average, with the same relative speed. Since A and B are different gases, each must have a different molar mass. If A has a higher molar mass than B, the particles of A must be hitting the sides of the container with more force. Thus the pressure in the container of gas A must be higher than that in the container with gas B. However, one of our initial assumptions was that the pressures were equal. Explain.

Find the area below the curve y=3/(9+x^2) from x=-3 to x=3

Write each expression in radical form, or write each radical in exponential form.

$$a ^ { \frac { 3 } { 4 } }$$

Express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t.

$$w = 2 y e ^ { x } - \ln z , \quad x = \ln \left( t ^ { 2 } + 1 \right) , \quad y = \tan ^ { - 1 } t , \quad z = e ^ { t }; \quad t = 1$$

How many water molecules are there in a swimming pool that is 15 m long, 8.5 m wide, and 1.5 m deep?

You have helium gas in a two-bulbed container connected by a valve as shown below. Initially, the valve is closed.
a. When the valve is opened, will the total pressure in the apparatus be less than $5.00 \mathrm{~atm}$, equal to $5.00 \mathrm{~atm}$, or greater than $5.00 \mathrm{~atm}$? Explain your answer.

_____ is the amount of matter in an object.

A chemistry student relates the following story: "I noticed my tires were a bit low and went to the gas station. As I was filling the tires, I thought about the kinetic molecular theory (KMT), and I realized that I was increasing both the pressure and volume of the tires as I filled the tires with air. 'Hmmm,' I thought, 'that goes against what I learned in chemistry, where I was told pressure and volume are inversely proportional." What is the fault of the logic of the chemistry student in this situation? Explain why we think pressure and volume to be inversely related (draw pictures and use the KMT).

As you increase the temperature of a gas in a sealed, rigid container, what happens to the density of the gas? Would the results be the same if you did the same experiment in a container with a piston at constant pressure? Explain.

A swimmer wants to swim straight across a river with current flowing at a speed of $v _ { 1 } = 0.350 \mathrm { m } / \mathrm { s }$ . If the swimmer swims in still water with speed $v _ { 2 } = 1.25 \mathrm { m } / \mathrm { s }$ at what angle should the swimmer point upstream from the shore, and at what speed will the swimmer swim across the river?

Solve:

$$\frac { 1 } { 5 } + \frac { 1 } { 2 } x = \frac { 3 } { 20 }$$

In lines 101-131, underline descriptions of changes in the way the narrator feels about her husband.

Nitrogen gas $\left( \mathrm { N } _ { 2 } \right)$ reacts with hydrogen gas $\left( \mathrm { H } _ { 2 } \right)$ to form ammonia gas $\left( \mathrm { NH } _ { 3 } \right).$ You have nitrogen and hydrogen gases in a 15.0-L container fitted with a movable piston (the piston allows the container volume to change so as to keep the pressure constant inside the container). Initially, the partial pressure of each reactant gas is 1.00 atm. Assume the emperature is constant and the reaction goes to completion. Calculate the volume of the container after the reaction has reached completion.

Nitrogen gas $\left( \mathrm { N } _ { 2 } \right)$ reacts with hydrogen gas $\left( \mathrm { H } _ { 2 } \right)$ to form ammonia gas $\left( \mathrm { NH } _ { 3 }\right).$ You have nitrogen and hydrogen gases in a 15.0-L container fitted with a movable piston (the piston allows the container volume to change so as to keep the pressure constant inside the container). Initially, the partial pressure of each reactant gas is 1.00 atm. Assume the temperature is constant and the reaction goes to completion. Calculate the partial pressure of ammonia in the container after the reaction has reached completion.