Convert  to

Use Gay-Lussac's law:

Plug in values:

Using the equation for the root-mean-square speed:

is the temperature in Kelvin

is the molar mass of the gas, in kilograms per mole

Converting Celsius to Kelvin and plugging in values:

We will start with the ideal gas law for this problem:

Since the problem statement is asking us for a change in density, we will need to manipulate the ideal gas law to get this unit. We will start by multiplying both sides of the expression by the molecular weight of nitrogen:

Now rearranging we get:

We can apply this to both scenarios, with density, pressure, and temperature being the only changing variables: 

Dividing the second expression by the first and eliminating common variables, we get:

Plugging in our values and making sure our temperatures are in Kelvin, we get:

Using

is the temperature in Kelvin

is the gas constant

is the molar mass in kilograms

Converting to Kelvin:

It can be seen that this increase in temperature would lead to a very modest increase in velocity.

Use the following equation to find the average velocity:

Where 

is the temperature in Kelvin

is the molar mass of the gas, in kilograms

Converting Celsius to Kelvin and plugging in values:

Using

is the temperature in Kelvin

is the gas constant

is the molar mass in kilograms

Converting to Kelvin and plugging in values:

Using,

Where

 is the Boltzmann constant, 

 is the temperature, in Kelvin

 is the mass of a single molecule, in kilograms

Finding mass of a single oxygen molecule:

Plugging in values:

Using,

Where

 is the Boltzmann constant, 

 is the temperature, in Kelvin

 is the mass of a single molecule, in kilograms

Finding mass of a single chlorine molecule:

Plugging in values:

For this question, we're asked to identify a statement that is false with respect to ideal gasses. Let's look at each.

There are a number of assumptions that are put into place when defining an ideal gas, together which are called the kinetic molecular theory of ideal gasses.

For one, each gas particle is assumed to exert no attractive or repulsive forces with any other gas particle. As these particles move in constant motion, they continuously collide both with themselves and with the wall of their container. Each of these collisions is assumed to be perfectly elastic, such that no energy is lost or gained from the collision and energy is perfectly maintained. Furthermore, the size of the individual gas particles is assumed to be so tiny as to be negligible. What this means is that the overall amount of space taken up by the gas particles is negligible with respect to the amount of space in the container.

Although the volume of each gas particle is assumed to be negligible, the same cannot be said about their mass. Each particle has a characteristic mass that is dependent on the identity of the gas.

We will use the combined gas law:

With "1" referring to Mt Whitney, and "2" referring to Death Valley, we can rearrange the equation to get 

We need to convert both temperatures to Kelvin

We plug in our values.