Calculate the rms speeds of CO and

$$Cl_2$$

molecules at 300 K.

Layla is thinking of a positive, single-digit, even number. Luis guesses it is 7. a. What is the sample space? b. What is the probability that Luis's guess is correct?

Calculate the rms speed for CO molecules at $25~^o\text{C}$. What is the ratio of this speed to that of Ar atoms at the same temperature?

Suppose you have two 1-L flasks, one containing

$$N_2$$

at STP, the other containing

$$CH_4$$

at STP. How do these systems compare with respect to number of molecules.

Place the following gases in order of increasing average molecular speed at

$$300 \mathrm { K } : \mathrm { CO } , \mathrm { SF } _ { 6 } , \mathrm { H } _ { 2 } \mathrm { S } , \mathrm { Cl } _ { 2 } , \mathrm { HBr }$$

Determine whether each of the following changes will increase, decrease, or not affect the rate with which gas molecules collide with the walls of their container: increasing the temperature

The speed of sound in different gases at a certain temperature T depends on the molar mass of the gases. Show that

$${\frac{v_1}{v_2}} = \sqrt{\frac{M_2}{M_1}},$$

where

$$v_1$$

is the speed of sound in a gas of molar mass

$$M_1$$

and

$$v_2$$

is the speed of sound in a gas of molar mass

$$M_2$$

.

Give the two elements that are liquids and the five (other than the six noble gases) that are gases at room temperature and atmospheric pressure.

Which halogens are gases at room temperature and atmospheric pressure?

Olympic cyclists fill their tires with helium to make them lighter. Calculate the mass of air in an air-filled tire and the mass of helium in a helium-filled tire. What is the mass difference between the two? Assume that the volume of the tire is 855 mL, that it is filled to a total pressure of 125 psi, and that the temperature is 25$^{\circ} C$. Also, assume an average molar mass for air of 28.8 g/mol.

What is the mole fraction of $\mathrm{C}_3 \mathrm{H}_8$ (g) in the flask before reaction?

Consider a unit vector u in $\mathbb R^3,$ We define the matrices

$$\begin{array} { c } { A = 2 u u ^ { T } - I _ { 3 } \quad \text { and } \quad B = I _ { 3 } - 2 u u ^ { T } } \end{array}$$

Describe the linear transformations defined by these matrices geometrically.

A 1.00 L flask is filled with 1.25 g of argon at 25 ∘C. A sample of ethane vapor is added to the same flask until the total pressure is 1.450 atm.

A) What is the partial pressure of argon, P(Ar), in the flask?
B) What is the partial pressure of ethane, P(ethane), in the flask?

A gas mixture at room temperature contains 10.0 mo! CO and 12.5 mol O2. (a) Compute the mole fraction of CO in the mixture. (b) The mixture is then hea ted, and the CO starts to react with the O2 to give CO2:

$$CO(g)+½O2(g)→CO2(g)$$

At a certain point in the heating, 3.0 mo! CO2 is present. Determin e the mole fraction of CO in the new mixture.