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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?
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And we’ve been given five expressions, one of which evaluates to the correct pressure.
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Before we go any further, let’s just break down some of these expressions to see what the numbers are.
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The number 0.087 appears in all the expressions.
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And it’s the amount of gas in moles.
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The number 0.0821 is the gas constant in units of liters atmospheres per kelvin per mole.
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You might be more familiar with the gas constant in terms of joules per kelvin per mole.
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But if you converted the units, the value in the expression would be correct.
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The number 295 corresponds to the temperature given in the question converted into kelvin: 22 plus 273.
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Although in one expression, the temperature appears in degrees Celsius.
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The last component of the expressions is the value 2.0 liters, which corresponds to the volume of our container.
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Now, let’s picture the gas inside the bottle, all 0.087 moles of it.
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The volume of the container is 2.0 liters and the temperature 22 degrees Celsius.
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These are all very ordinary conditions.
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So any gas under these conditions we can expect to behave like an ideal gas.
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The ideal gas law relates various properties of an ideal gas: the pressure, the volume, the amount in moles, and the temperature.
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And the gas constant allows us to get the correct numerical relationship between all these properties.
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For the ideal gas law to work, we need to be using temperature in absolute temperature scale, like the Kelvin scale.
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If we rearrange the ideal gas law in terms of pressure, this is what we get.
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Pressure equal to the amount in moles multiplied by the ideal gas constant multiplied by the temperature in kelvin divided by the volume.
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So let’s have a look at the expressions to see which one matches.
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Expression A has the amount in moles multiplied by the gas constant multiplied by the temperature in kelvin divided by the volume.
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If we evaluated the expression, we’d expect to get the pressure in atmospheres.
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This expression makes sense and matches what we would expect from the ideal gas law.
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But just in case, let’s have a look at the others.
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In the second expression, the volume and the amount are the wrong way around.
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In the third expression, it’s the volume and the temperature that are upside down.
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In the fourth expression, the volume and the gas constant are the wrong way up.
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And in the fifth expression, the temperature is given in the wrong units, degrees Celsius rather than kelvin.
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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.