## anonymous 4 years ago A compound consisting of only phosphorous and oxygen atoms is 43.64 % phosphorus by mass.The molecular mass/formula weight of the compound is 283.88 amu. How many phosphorous atoms ar in a molecule of this compound? Please show all calc involved.

1. anonymous

Since we know the percentage by mass of P in this compound, then we know the percentage by mass of O in the compound. From this, we can convert them into mols of each element and find out what the ratio is between them to determine the empirical formula. From the empirical formula, knowing the molar mass of the compound, we can determine the molecular formula. 43.64% P 56.36% O Now, making an assumption here that we have 1g of the substance will get us a long way. If we have 1g of substance, then we have...$43.64g(P)*\frac{1mol(P)}{30.974g(P)}=1.4089mol(P)$And...$56.36g(O)*\frac{1mol(O)}{15.999g(O)}=3.5227mol(O)$This is our ratio of elements in the compound. Now we just need to express these elements in terms of the element with the lowest amount compared to all other elements in the compound.$mols(O)=\frac{3.5527}{1.4089}=2.5216 \approx 2.5$$mols(P)=\frac{1.4089}{1.4089}=1$Now, to express these as whole numbers...$mols(O)=2.5*2=5$$mols(P)=1*2=2$Now we know that there are 5 oxygen atoms for every phosphorous atom, making the empirical formula for this compound...$P_2O_5$ Now, for the final step we need to convert this empirical formula into a molecular one. To do this, we need to find the ratio between the molar mass of the empirical formula and the molar mass of the actual compound, and that will give us a factor to multiply the empirical formula by...$MM_{P_2O_5}=141.943\frac{g}{mol}$$Ratio=\frac{283.88}{141.943}=1.99996 \approx 2$Now we know that the ratio is 2, so to make the molar mass of the molecular formula make sense with the molar mass given to us, we need to multiply the number of each atom in the compound by this factor of 2 to get the molecular formula...$P_4O_{10}$And from this we can deduce that there are (obviously) 4 atoms of phosphorous in this compound.

2. anonymous

wow thanks can you help me with some more please

3. anonymous

Post them up (:.

4. anonymous

5. anonymous

Well, according to the law of multiple proportions (and common sense), the subscripts of a compound must be whole numbers because there can't be a fraction of an atom present in a molecule. For instant, this is not a valid compound...$PO_{2.5}$So, to make the compound valid, we must find the smallest whole-number ratio of atoms that works, and we do this by multiplying the 2.5 O atoms by 2 to get 5. What we do to the O atoms we have to do to the P atoms, so we multiply both by 2. However, this only finds the empirical formula. The empirical formula is the smallest whole-number ratio of atoms that exists for a given compound. However, we compare the molar masses of the compound we found and the molar mass we are given in the problem, we see that they are not the same. To find the compound we want to find, we need to find out by what factor we need to multiply the empirical formula to get the correct molecular mass. Since the MM of the compound we found was about half the MM we were given, it makes sense that we need to multiply the entire empirical formula by 2 to make the molar masses match up. If we find the molar mass of the final compound we found, we will find that it will be very close to the MM we were given in the problem. You can do this as a check for yourself...$MM_{P_4O_{10}}=4(30.974\frac{g}{mol})+10(15.999\frac{g}{mol})=283.89\frac{g}{mol}$Which is only a hundredth off from the original value we were given for the MM of the compound. It's only off by this little amount because of rounding. It's close enough that we know for certain it's the molecular formula we are looking for.

6. anonymous

Does this make sense?