Question 3.EP.6: A sample of the explosive TNT (C7H5N3O6) has a mass of 650.5...
A sample of the explosive TNT (C_{7}H_{5}N_{3}O_{6}) has a mass of 650.5 g. How many moles of TNT are in this sample? How many molecules is this?
Strategy
We are asked to convert from mass to moles. So we must determine the molar mass of the substance and then use it to carry out the conversion. Once we know the number of moles, we can easily find the number of molecules since we know that one mole contains Avogadro’s number of molecules.
First we will calculate the molar mass of TNT.
Now we can use the molar mass to convert from mass to moles:
650.5 \ mol \ TNT\times \frac{1 \ mol \ TNT}{227.133 \ g \ TNT}=2.864 \ mol \ TNT
Finally, we can convert from moles to molecules using Avogadro’s number:
2.864 \ g \ TNT\times \frac{6.022\times 10^{23} \ molecules \ TNT}{1 \ mol \ TNT}=1.725 × 10^{24} \ molecules \ TNTAnalyze Your Answer
Admittedly, it is difficult to have an intuitive feeling for the number of molecules in any sample. In assessing our answer, we can begin by noting that it is a very large number. This makes sense because we are calculating the number of molecules in a macroscopic amount of TNT. We could also check a little more closely by looking at the intermediate step in which we found the number of moles. Because the molar mass of TNT is slightly larger than 200 g/mol, we should have roughly 3 moles in the 650-g sample. This is consistent with the value we found.
Discussion
The mass of this sample corresponds to a little less than 1.5 pounds, so the sample would probably be roughly the size of a brick. Note the enormous number of molecules in this fairly small amount of material.