Standard temperature and pressure is 0⁰C and 1 atm

Since we have the density of the mystery gas, we can rearrange the ideal gas law so that the remaining factors are equal to the density of the gas.

We can redefine moles of gas as mass over molar mass.

We can now rearrange the equation to solve for density (mass per volume), which is given in the question.

Using this set up and the values for standard temperature and pressure, we can solve for the molar mass.

Most gases exist as diatomic molecules in nature. , , and  are all common gases found in the atmosphere and the air we breathe.

Ozone, , is a rare exception to the diatomic bonding principle, and is also found in significant quantities in the atmosphere.

Monatomic oxygen, , has only six valence electrons and is relatively unstable; this compound would not be found naturally in the atmosphere.

This question does not acually deal with the ideal gas law, but only with the standard volume of a gas at STP. At standard temperature and pressure, one mole of gas has a volume of 22.5L.

We know that initially we have four moles of octane and excess oxygen. This means that octane will be the limiting reagent for the combustion reaction, since oxygen is in excess.

The total moles of reactant gas when utilizing all four moles of octane is 54, while the total moles of product gas is 68.

There is a total change in moles of:

Since we end the reaction with 14 more moles of gas than we started, the volume must increase:

The change in volume is .

The van't Hoff factor for CaCl₂ is 3 since the molecule dissociates in solution to 3 ions. T is in absolute temperature (25+273=298). This makes the osmotic pressure:

3*2M*0.082*298.

We use the ideal gases equation to know the mol of water we need in the gas phase to generate a pressure of  in a  flask at .

And the mass is:

If we have less than that amount of water the liquid will evaporate completely but there will not be enough molecules to reach the vapor pressure. More than  of water will allow to reach the vapor pressure and there will be also a liquid leftover. Remember that the vapor pressure of a liquid at a fixed temperature is a constant.

Using the molecular mass we calculate the number of mol of  :

At this moment we could apply the percentage yield, however let's live it for the end. Each mole of  decomposed will generate  of gas. Then the total pressure assuming  yield will be:

Since only  of the  decomposes, the real total pressure will be:

First, identify the necessary parameters.

We must use the ideal gas equation:

 and since the molar gas constant given uses Kelvin in it's definition, we must convert  to Kelvin as follows: 

Since the pressure given is gauge pressure, we must convert to the actual pressure as follow: 

So therefore the pressure we want to use is 

Now that we have listed the given quantities we can see that in order to get the mass of  needed, we must first find the number of moles of  needed to fill the volume of the airbag, then use the molar ratios from the above chemical equation to convert moles of  to moles of , after which we can use the molar mass of  to calculate the grams of  needed to inflate the airbag.

In order to calculate the number of moles of  we can employ the Ideal gas law: to find n (the number of moles of gas; which in this case the only gas involved is 

Plug in the given quantities that have been converted into the correct units and quantities:

Solve.

Now that we know the moles of  needed we can use stoichiometry, and the information in the following equation: 

To determine the number of moles of  required and then convert the moles of  to the grams of  using the molar mass of . The molar mass of  can be found by using a periodic table and adding the molar masses of the constituent elements as shown below:

Molar mass of

Given that we calculated the moles of  to fill the volume of the airbag to be:  , and the molar ratios from the chemical equation we can set up the final steps of the calculation as shown below:

Therefore in order to inflate this driver's side airbag it would need to contain at least 68.04g of 

In this question, we're given the mass and volume of an unknown hydrocarbon filling a container. We're asked to determine the identity of this compound.

To solve this problem, it's important to realize that for any ideal gas at STP (standard temperature and pressure),  of the gas will equate to  of that gas. For this question, we're told that there is  present. 

Now that we know how many moles of gas are in the container, we can use this information, together with the mass provided to us in the question stem, to determine the molecular mass of the unknown compound.

Looking at the answer choices, the only hydrocarbon that matches this molecular mass is ethane, .

The ideal gas law assumes the gas particles are non-interacting and small relative to the size of their container.  At 200K (lowest temperature in the list, and the highest pressure).  This gives Ar the most time to interact due to molecular speeds and the high pressure implies the molecular size is not insignificant relative to the container.