the mass of a certain mixture of BaO and CaO is found to be exactly one half that of the mixed sulfates formed from it by the action of H2SO4. calculate the percentage of BaO and CaO in the mixture.
An interesting problem.
Three equation and three unknowns but we can work it around with just two since these are related.
Let X = mass BaO
and Y = mass CaO
and mm stand for molar mass.
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eqn 1 is X + Y = mass whatever that may be.
Convert to sulfates and you have eqn 2.
(mm BaSO4/mm BaO)*X + (mm CaSO4/mm CaO)*Y = 2*mass whatever that is.
Make up a convenient number for mass X + Y and it really makes no difference what number you choose. I chose 1 to make it easier.
Solve for X and Y; then
%BaO = (X/1)*100 = ? (I obtained about 47%)
%CaO = (Y/1)*100 = ?(I obtained about 53%) but these were just quick calculations. You need to go thorought it more carefully. By the way, most students "shudder" at the thought of making up a number to use for mass BUT try it. Use it with 1 for mass, then change it to 2 or 3 or 4 or whatever you choose and work the problem. X and Y will always come out different, of course, BUT the problem doesn't ask for BaO and CaO. It asks for PERCENT and the percent will always come out the same.
To calculate the percentage of BaO and CaO in the mixture, we need some additional information. Specifically, we need the relative atomic masses (or molar masses) of BaO, CaO, and the mixed sulfates. Once we have these values, we can use the concept of stoichiometry to determine the percentages.
Step 1: Determine the molar masses:
Let's say the molar mass (atomic mass) of BaO is M_barium and the molar mass of CaO is M_calcium.
Step 2: Write balanced equations for the reactions:
The reaction of BaO with H2SO4 will produce barium sulfate (BaSO4):
BaO + H2SO4 → BaSO4 + H2O
The reaction of CaO with H2SO4 will produce calcium sulfate (CaSO4):
CaO + H2SO4 → CaSO4 + H2O
Step 3: Use stoichiometry to relate the masses:
According to the problem, the mass of the mixture of BaO and CaO is half that of the mixed sulfates (BaSO4 and CaSO4) formed from them. Let's denote the mass of the mixture as M_mixture and the mass of the mixed sulfates as M_sulfates.
We can set up the following equation:
M_mixture = (1/2) * M_sulfates
Step 4: Apply stoichiometry to calculate the molar masses of the mixed sulfates:
The molar mass of a compound is the sum of the molar masses of its constituent elements.
Let's assume the molar mass of BaSO4 is M_ba_sulfate and the molar mass of CaSO4 is M_ca_sulfate.
M_sulfates = M_ba_sulfate + M_ca_sulfate
Step 5: Calculate the percentages of BaO and CaO in the mixture:
To find the percentage of each compound, we need to calculate the masses of BaO and CaO in the mixture first.
Let the mass of BaO in the mixture be M_ba_oxide and the mass of CaO in the mixture be M_ca_oxide.
M_ba_oxide = (M_ba_sulfate / M_sulfates) * (1/2) * M_mixture
M_ca_oxide = (M_ca_sulfate / M_sulfates) * (1/2) * M_mixture
The percentage of BaO in the mixture can then be calculated as:
Percentage of BaO = (M_ba_oxide / M_mixture) * 100
The percentage of CaO in the mixture can be calculated as:
Percentage of CaO = (M_ca_oxide / M_mixture) * 100
Step 6: Substitute the values and calculate the percentages:
To solve this problem, we need the molar masses of BaO, CaO, BaSO4, and CaSO4. These values can be found in a periodic table or reference book.