An ideal gas with a pressure of  is is compressed to  of its original volume, what is the new pressure?

Use Boyle’s law:

You want to solve for the new pressure so isolate :

It compresses to  its original volume so, 

Plug in everything we know:

Cancel  from the numerator and denominator

Use Boyle’s law:

You want to solve for the new pressure so isolate :

It expands to  its original volume, so 

Plug in everything we know:

Cancel  from both the numerator and denominator

Use the combined gas law:

Solve for  since that is the new volume for which we need to solve:

Since we have the total pressure and the pressures of helium and nitrogen, we can find the pressure of neon in this container.

Next, convert this pressure into atmospheres.

Now, recall the Ideal Gas Law:

Rearrange the equation to solve for moles of gas:

Using the pressure of neon, find the moles of neon that is present in the container.

Finally, convert the moles of neon into grams of neon using the molar mass.

Make sure your answer has  significant digits.

For this question, we're told that a chemical reaction is producing hydrogen gas. In doing so, the gas is displacing a certain amount of water vapor. We're asked to determine the number of moles of gas produced in this process.

The amount of water displaced by the production of hydrogen gas will be the amount (volume) of hydrogen gas produced. To measure its pressure, we take the reading of the total pressure and then subtract from it the pressure of water vapor (since it contributes to the total pressure). Using this information, we can use the ideal gas equation to determine the number of moles of hydrogen gas.

Next, we can use the ideal gas equation to solve for our answer.

To start, first recognize that this is an ideal gas law problem

Rearranging the equation to solve for P gives us

To solve the problem, we now need to find the total number of moles in the gaseous mixture n_tot. To do this, convert the values for Ne and He to moles and add them together

Now that we have n_tot, plug known values into the ideal gas law equation. Remember to convert from Celsius to Kelvin!

This is another ideal gas law problem, but this time dealing with partial pressures. Total pressure of a mixture is the sum of the partial pressures of each component. So first calculate the partial pressure exerted by 

Now that we have solved for the partial pressure of , we can solve for moles of  by using the ideal gas law equation

Rearrange to solve for moles of 

This equation explicitly shows how the rate of effusion is inversely proportional to the molar mass of a gas in a gaseous solution. 

Because , time relates to molar mass by: 

Simplifying this equation, we see that: 

As a result, time relates directly to molar mass

Recall Graham's Law of Effusion for two gases, A and B:

From the equation, we know the following:

Thus, we can solve for the molar mass of the unknown gas. Let  be the molar mass of the unknown gas.

Make sure that your answer has  significant figures.

We're being asked to compare the effusion rates of oxygen and carbon dioxide.

Remember that effusion is the spontaneous movement of a gas through a small hole from one area to another. It's worth noting that at a given temperature, the average speed of all gas molecules in a system is used to calculate the average kinetic energy of the gas particles. This dependence of kinetic energy on temperature means that at a given temperature, any gas particle will have the same kinetic energy.

In this case, we can say that the kinetic energy of oxygen molecules in one system is equal to the kinetic energy of carbon dioxide molecules in another system. Furthermore, since mass is inversely proportional to velocity, identical kinetic energies would mean that as the mass of the gas particles in a system decreases, their velocity (and thus, effusion rates) would increase.

We can use this information to solve for the relative effusion rates between oxygen and carbon dioxide. By setting their kinetic energies equal to each other, we can derive an expression that relates their relative speeds to their relative masses.

Generally speaking, this expression shows how the velocity of any two gasses depends on their mass. In this case, the gasses are oxygen and carbon dioxide.

We can use the periodic table of the elements to find out the mass of each gas, and use that information to calculate the relative effusion rates.

This shows that oxygen will effuse at a rate that is about  faster than carbon dioxide.