Based on the balanced equation
2Ba + O2 → 2BaO
calculate the number of BaO formula units formed when 142 Ba atoms and 73 O2 molecules react?
You know it's a limiting reagent problem when both of the starting materials are given. You must determine which is the limiting reagent.
Two calculations will do it.
142 Ba x (2 moles BaO/2 moles Ba) = 142 x 1/1 = 142 BaO molecules formed.
73 O2 x (2 moles BaO/1 moles O2) = 73 x (1/2) = 146 BaO molecules formed.
Both answers can't be correct; the correct one is ALWAYS the smaller. Therefore Ba is the limiting reagent and 142 BaO molecules (formula units) will be formed. Some of the oxygen will remain unreacted. You can determine how much is left easily.
142 Ba atoms x (1 mole O2/2 moles BaO) = 142 x (1/2) = 71 molecules O2 used. We had 73 initially; therefore, 73-71 = 2 molecules O2 remain unreacted.
First, we need to determine the limiting reactant - the reactant that will be completely consumed and determine the amount of product formed.
To find the limiting reactant, we compare the amounts of each reactant to the stoichiometric ratio in the balanced equation.
From the balanced equation:
2 mol Ba reacts with 1 mol O2 to produce 2 mol BaO.
We start by converting the given amounts of Ba and O2 into moles:
Number of moles of Ba = 142 Ba atoms / (1 mol Ba atoms) = 142 mol Ba
Number of moles of O2 = 73 O2 molecules / (1 mol O2 molecules) = 73 mol O2
Next, we compare the moles of Ba and O2 based on the stoichiometric ratio. Since the ratio is 2:1 (Ba:O2), we need half the number of moles of O2 as compared to Ba to react completely.
Number of moles of O2 required = 0.5 * Number of moles of Ba = 0.5 * 142 mol Ba = 71 mol O2
Now, we compare the actual number of moles of O2 to the required moles. If the actual moles of O2 are greater than the required moles, then Ba is the limiting reactant. If the actual moles of O2 are less than the required moles, then O2 is the limiting reactant.
Actual moles of O2 = 73 mol O2
Since 73 mol O2 > 71 mol O2, Ba is the limiting reactant.
Now we can calculate the moles of BaO formed. From the stoichiometry, we know that 2 moles of BaO are formed for every 2 moles of Ba.
Moles of BaO formed = Number of moles of Ba * (2 moles BaO / 2 moles Ba)
= 142 mol Ba * (2 mol BaO / 2 mol Ba)
= 142 mol BaO
Finally, we convert the moles of BaO formed to the number of BaO formula units, using Avogadro's number (6.022 x 10^23 formula units/mol).
Number of BaO formula units formed = Moles of BaO formed * Avogadro's number
= 142 mol BaO * (6.022 x 10^23 formula units/mol)
= 8.56 x 10^25 BaO formula units
Therefore, when 142 Ba atoms and 73 O2 molecules react, 8.56 x 10^25 BaO formula units are formed.
To calculate the number of BaO formula units formed, we need to determine the limiting reactant out of Ba and O2. The limiting reactant is the one that will be completely consumed, thereby determining the maximum amount of product that can be formed.
To find the limiting reactant, we need to compare the stoichiometry (coefficients) of Ba and O2 in the balanced equation.
From the balanced equation: 2Ba + O2 → 2BaO
- The stoichiometry between Ba and O2 is 2:1, meaning that two moles of Ba react with one mole of O2 to produce two moles of BaO.
- One mole of any substance is equal to 6.022 x 10^23 formula units.
First, let's calculate the number of moles for Ba and O2 given the number of atoms and molecules:
Number of moles of Ba = 142 Ba atoms / 6.022 x 10^23 Ba atoms/mol
Number of moles of Ba = 0.236 mol
Number of moles of O2 = 73 O2 molecules / 6.022 x 10^23 O2 molecules/mol
Number of moles of O2 = 0.121 mol
Now, let's compare the stoichiometry (coefficients) of Ba and O2 in the balanced equation:
The stoichiometry of Ba and O2 is 2:1, meaning that for every 2 moles of Ba, we need 1 mole of O2 to react completely.
Since we have 0.236 mol of Ba and 0.121 mol of O2, we see that O2 is the limiting reactant because we require twice the number of moles of O2 (0.242 mol) for complete reaction with the given moles of Ba.
Next, let's calculate the number of moles of BaO formed. Since each mole of O2 produces 2 moles of BaO:
Number of moles of BaO = 2 moles of O2 * 2 moles of BaO / 1 mole of O2
Number of moles of BaO = 4 mol
Finally, let's convert the number of moles of BaO to formula units by multiplying by Avogadro's number:
Number of formula units of BaO = 4 mol * 6.022 x 10^23 formula units/mol
Number of formula units of BaO = 2.409 x 10^24
Therefore, there are 2.409 x 10^24 BaO formula units formed when 142 Ba atoms and 73 O2 molecules react.