Video: Identifying the Expression That Yields the Pressure Exerted by a Given Amount of Gas, in a Given Volume, at a Given Temperature in a Set of Expressions

What is the pressure exerted by 0.087 moles of gas present in a closed bottle that has a volume of 2.0 liters at 22°C? [A] ((0.087 mol)(0.0821 L ⋅ atm/K ⋅ mol)(295 K))/(2.0 L) [B] ((2.0 L)(0.0821 L ⋅ atm/K ⋅ mol)(295 K))/(0.087 moles) [C] ((2.0 L)(0.0821 L ⋅ atm/K ⋅ mol)(0.087 mol))/(295 K) [D] ((2.0 L)(295 K)(0.087 mol))/(0.0821 L ⋅ atm/K ⋅ mol) [E] ((0.087 mol)(0.0821 L ⋅ atm/K ⋅ mol)(22°C))/(2.0 L)

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Video Transcript

What is the pressure exerted by 0.087 moles of gas present in a closed bottle that has a volume of 2.0 liters at 22 degrees Celsius?

And we’ve been given five expressions, one of which evaluates to the correct pressure. Before we go any further, let’s just break down some of these expressions to see what the numbers are. The number 0.087 appears in all the expressions. And it’s the amount of gas in moles. The number 0.0821 is the gas constant in units of liters atmospheres per kelvin per mole. You might be more familiar with the gas constant in terms of joules per kelvin per mole. But if you converted the units, the value in the expression would be correct. The number 295 corresponds to the temperature given in the question converted into kelvin: 22 plus 273. Although in one expression, the temperature appears in degrees Celsius. The last component of the expressions is the value 2.0 liters, which corresponds to the volume of our container.

Now, let’s picture the gas inside the bottle, all 0.087 moles of it. The volume of the container is 2.0 liters and the temperature 22 degrees Celsius. These are all very ordinary conditions. So any gas under these conditions we can expect to behave like an ideal gas. The ideal gas law relates various properties of an ideal gas: the pressure, the volume, the amount in moles, and the temperature. And the gas constant allows us to get the correct numerical relationship between all these properties. For the ideal gas law to work, we need to be using temperature in absolute temperature scale, like the Kelvin scale.

If we rearrange the ideal gas law in terms of pressure, this is what we get. Pressure equal to the amount in moles multiplied by the ideal gas constant multiplied by the temperature in kelvin divided by the volume. So let’s have a look at the expressions to see which one matches.

Expression A has the amount in moles multiplied by the gas constant multiplied by the temperature in kelvin divided by the volume. If we evaluated the expression, we’d expect to get the pressure in atmospheres. This expression makes sense and matches what we would expect from the ideal gas law. But just in case, let’s have a look at the others.

In the second expression, the volume and the amount are the wrong way around. In the third expression, it’s the volume and the temperature that are upside down. In the fourth expression, the volume and the gas constant are the wrong way up. And in the fifth expression, the temperature is given in the wrong units, degrees Celsius rather than kelvin.

So if we evaluated expression A, we’d get the pressure exerted by 0.087 moles of gas in a closed two-liter bottle at 22 degrees Celsius.

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