Question

How many molecules are in \[75.0g\] of diphosphorus pentoxide \[{P_2}{O_5}\] ?

Answer 1

Hint: Here the question is about asking how many molecules are there in the given compound so that at first we actually need to calculate molar quantity of given compound. After doing this, we will be getting a particular number of moles. Hence we need to convert the particular number of moles to a number which is asked as per question. Here we need to remind another thing that the amount of substance is measured in moles.

Formula used: Molar quantity \[ = \dfrac{{Mass}}{{Molarmass}}\]
Mass and molar mass will be according to the given particular compound.

Complete step-by-step answer:
First of all our duty here is to find the molar quantity of diphosphorus pentoxide.
The equation for molar quantity is as follows,
Molar quantity \[ = \dfrac{{Mass}}{{Molarmass}}\]
So let us write down the values of mass and molar mass of \[{P_2}{O_5}\].
Here the given mass of \[{P_2}{O_5}\] \[ = 75.0g\]
The molar mass value of \[{P_2}{O_5}\]\[ = 141.94.g.mo{l^{ - 1}}\]
Next we shall substitute the values in the above equation.
So, equation of molar quantity will be as follows,
Molar quantity \[ = \dfrac{{75.0.g}}{{141.94.g.mo{l^{ - 1}}}} = 0.528mol\]
\[{P_2}{O_5}\]is of course having molar mass of \[141.94.g\] . Actually we have to know that the molecule is \[{P_4}{O_{10}}\] . But we don’t have to bother about this matter in this treatment.

Next, our duty to convert the above number of moles to a number. For that we have to keep a point as a reminder as it is always a fact that \[1mole\] of a particular stuff is having \[6.022 \times {10^{23}}\] individual substances in it. So this will provide us a logic idea that if one mole is having Avogadro number of particles in that, then for finding number of molecules in \[0.528mol\] we have to do the calculation as following,
\[0.528mol \times 6.022 \times {10^{23}}mo{l^{ - 1}}\] which is equal to individual \[{P_2}{O_5}\]

Therefore , \[0.528mol \times 6.022 \times {10^{23}}mo{l^{ - 1}} = 3.179 \times {10^{23}}\] molecules.
Hence, \[3.179 \times {10^{23}}\] molecules are in \[75.0g\] of diphosphorus pentoxide \[{P_2}{O_5}\] .

Note: First of all, the major step we have to keep in mind regarding this question is that we should not only find the molar quantity here but also should convert the number of moles to a number. Then only the answer will be complete as it is asking about how many molecules. Next , the important point to note out is one mole of a substance is having Avogadro number of individual particles. Actually we use this logic point to convert to a number of molecules. This point can be very useful in determining the number of molecules of any particular compound. Also, remember always that mole is actually a unit of measurement of amount of substance.