### Video Transcript

What is the molar volume of a gas at room temperature and pressure, to two significant figures?

The molar volume is the volume occupied per mole of gas. Mathematically, we can represent the molar volume, or 𝑉 𝑚, as the volume of the gas divided by the amount of gas in moles. Since the volume of a gas varies with temperature and pressure, these must both be specified to find the molar volume. In this question, the temperature and pressure is room temperature and pressure, which you may sometimes see as RTP. Room temperature and pressure is defined as 20 degrees Celsius and one atmosphere.

We’re going to use the ideal gas law to solve this problem. While not all gases behave ideally, the deviations from ideal behavior are small at room temperature and pressure. So, we don’t have to worry about them to solve this problem. We’re looking for an expression for the molar volume, or the volume divided by the amount of gas in moles. Which we can find by rearranging the ideal gas law.

With this expression, all we need to do is plug everything in to find our answer. 𝑅 is the ideal gas constant, which has different expressions depending on the units. We want the form of the constant that has units with liters, atmospheres, mole, and kelvin to match the problem. So, the expression of the ideal gas constant we want is 0.08206 liters times atmospheres per mole per kelvin.

The temperature given in the problem is 20 degrees Celsius, but we want the units to match the units in the ideal gas constant. So, we need to convert to kelvin. We can do this by adding 273 to our temperature, giving us a temperature in kelvin of 293. Finally, the pressure is one atmosphere.

Solving for the molar volume, we get an answer of 24.04 liters per mole. Rounding to two significant figures, we get an answer of 24 liters per mole. The result of this calculation tells us that any gas behaving ideally will have the same molar volume at the same temperature and pressure.

In other words, if we had two identical 24-liter flasks both at room temperature and pressure with one containing hydrogen gas, which is an extremely light gas with the molar mass of about two grams per mole. And the other flask containing sulphur hexafluoride, which is a very dense and heavy gas with the molar mass of about 146 grams per mole. Even though these flasks both contain very different gases, each flask would contain about one mole of gas. This is because the volume a gas occupies is largely determined by the number of molecules of gas and not the type of molecules of gas.