A sample of gas at zero degrees Celsius and one atmosphere occupied 16.8 litres of space. The number of molecules it contained was blank.
Rather than numbers to choose from, we’ve been given five expressions. The way these expressions are constructed may help us figure out which method is being used to produce them. Let’s have a look at the expressions to see if we can figure out what any of the parts are. 6.02 times 10 to the 23 is Avogadro’s number to three significant figures. We find Avogadro’s number in the description of a mole. One mole is equal to an Avogadro’s number of something.
What this suggests is that the question should allow us to figure out the number of moles of particles of gas based on the conditions. So let’s have a think. The conditions of zero degrees Celsius and one atmosphere is very close to the conditions for standard temperature and pressure, one bar and zero degrees Celsius. We know that one mole of an ideal gas at standard temperature and pressure will have a volume of 22.4 litres. This is sometimes expressed using the molar volume, 𝑉 𝑚, equal to 22.4 litres for every mole.
This value can alternatively be determined using the ideal gas equation, where we have 𝑉 over 𝑛, which gives us our molar volume, in terms of 𝑅, 𝑇, and 𝑃, the gas constant, the temperature in Kelvin, and the pressure. Now we’re in a better position to understand the significance of the other numbers in the expressions.
We have Avogadro’s number. Therefore, the other number must have something to do with the number of moles. To work out the amount of gas we have, we have to start with its volume. We know that, for an ideal gas, the volume is directly proportional to the number of moles. If we divide the volume by the molar volume, we should get the number of moles, so 16.8 litres multiplied by one mole per 22.4 litres.
This simplifies to three-quarters of a mole, or 0.75 moles. We can then figure out the number of molecules by multiplying the amount in moles by Avogadro’s constant, which tells us the number of entities per mole, 6.02 times 10 to the 23. That gives us this expression. And if we cancel units of moles, we get this expression, 0.75 times Avogadro’s number. This corresponds with option A.
So for a sample of gas at zero degrees Celsius and one atmosphere, if it occupies 16.8 litres of space, the number of molecules it contains would be 0.750 multiplied by 6.02 times 10 to the 23 molecules.