Question

Question #a1c07

Answer 1

`=8.97xx10^22 C_3H_8 " molecules"`

Explanation:

1. Write the balanced equation

   `C_3H_8(g)+5O_2(g)->3CO_2(g)+4H_2O(g)`

2. Assuming that the `CO_2` gas produced from the reaction behaved ideally; thus, the relationship that `"1mol of any ideal gas occupies a volume of 22.4L"` is the equivalence statement needed to find the unknown variable and can be interpreted as:

   `"1mol of any ideal gas"` `-=22.4L` `"of any ideal gas"`

3. Given the desired volume of `CO_2`; that is, 10.0L and the relationship described above, it can be deduced that the number of moles `(eta)`:

   `eta=10.0cancel(L*CO_2)xx(1molCO_2)/(22.4cancel(L*CO_2))=0.446molCO_2`

4. Now, find the number of moles of `C_3H_8`. To convert `etaCO_2` to `etaC_3H_8`, refer to the balanced equation for the mole ratio; i.e.,

   `=0.446cancel(molCO_2)xx(1molC_3H_8)/(3cancel(molCO_2))`
   `=0.149molC_3H_8`

5. Knowing the number of moles of `C_3H_8`, the number of molecules can be obtained through the relationship:

   `"1mol of " C_3H_8` `-=6.02xx10^23C_3H_8 " molecules"`

6. Now, using the preceding equivalence statement where a suitable conversion factor is obtainable, the number of molecules of `C_3H_8` is;

   `=0.149cancel(molC_3H_8)xx(6.02xx10^23C_3H_8 " molecules")/(1cancel(molC_3H_8))`
   `=0.897xx10^23C_3H_8" molecules"`
   `=8.97xx10^22C_3H_8 " molecules"`