Consider the following reaction,
4 PH3(g) + 8 O2(g) → P4O10(s) + 6 H2O(g)
If a container were to have 32 molecules of PH3 and 32 molecules of O2 initially, how many total molecules (reactants plus products) would be present in the container after this reaction goes to completion? (Use only whole numbers to solve.)
To solve this problem, we need to determine the stoichiometry of the reaction, which relates the number of molecules of the reactants to the number of molecules of the products.
According to the balanced equation:
4 PH3(g) + 8 O2(g) → P4O10(s) + 6 H2O(g)
The stoichiometry tells us that for every 4 molecules of PH3 and 8 molecules of O2, we produce 1 molecule of P4O10 and 6 molecules of H2O.
Given that we initially have 32 molecules of PH3 and 32 molecules of O2, we can determine the limiting reactant. The limiting reactant is the one that will be completely consumed in the reaction, thus determining the maximum amount of product formed.
Let's compare the number of moles of PH3 and O2:
Moles of PH3 = Number of molecules of PH3 / Avogadro's number
= 32 / 6.022 x 10^23
= 5.31 x 10^-23 moles of PH3
Moles of O2 = Number of molecules of O2 / Avogadro's number
= 32 / 6.022 x 10^23
= 5.31 x 10^-23 moles of O2
According to the stoichiometry, for every 4 moles of PH3, we need 8 moles of O2. Since the moles of PH3 and O2 are equal, both reactants will be completely consumed.
Now, let's calculate the number of product molecules formed:
Moles of P4O10 = (5.31 x 10^-23 moles of PH3) / (4 moles of PH3) x (1 mole of P4O10)
= 1.33 x 10^-23 moles of P4O10
Moles of H2O = (5.31 x 10^-23 moles of PH3) / (4 moles of PH3) x (6 moles of H2O)
= 7.98 x 10^-23 moles of H2O
Finally, we can convert the moles of product to the number of molecules:
Number of P4O10 molecules = Moles of P4O10 x Avogadro's number
= 1.33 x 10^-23 x 6.022 x 10^23
≈ 8 molecules of P4O10
Number of H2O molecules = Moles of H2O x Avogadro's number
= 7.98 x 10^-23 x 6.022 x 10^23
≈ 48 molecules of H2O
Now, to find the total number of molecules after the reaction, we add the number of reactant molecules and the number of product molecules:
Total number of molecules = 32 molecules of PH3 + 32 molecules of O2 + 8 molecules of P4O10 + 48 molecules of H2O
= 120 molecules
Therefore, after the reaction goes to completion, there would be a total of 120 molecules in the container.