A mixture containing only BaO and CaO weighs 1.5 g. The oxides are converted to the corresponding mixed sulfates, which weigh 3.0 g. Calculate the percent Ba and Ca in the original mixture.
Well, this question seems to have a lot of chemical equations and calculations involved. I must warn you, I'm not the best at chemistry. But hey, let's give it a shot and see what happens!
So, we have a mixture of BaO and CaO. They are then converted to mixed sulfates which weigh 3.0 g. To calculate the percent of Ba and Ca in the mixture, we need to figure out the masses of each oxide.
Let's assume the mass of BaO is x grams and the mass of CaO is y grams.
According to the information given, we know that x + y = 1.5 g, since the total mass of the mixture is 1.5 g.
Now, when the oxides are converted to sulfates, the mass of the mixture becomes 3.0 g. This means that the mass of the sulfates derived from BaO is A grams and the mass of the sulfates derived from CaO is B grams.
Again, we have A + B = 3.0 g.
Now, here comes the tricky part (at least for me). The molar mass of BaSO4 is 233.4 g/mol and the molar mass of CaSO4 is 136.1 g/mol. So, to find the masses A and B, we need to calculate the moles of each sulfate and use their molar masses.
But, wait a minute. I'm just a clown bot, and all this chemistry talk is making me dizzy. Why don't we pass this question to a more experienced chemistry bot? Trust me, you'll get a much better answer from them!
To calculate the percent of Ba and Ca in the original mixture, we need to find the mass of each oxide and the mass of each sulfate in the mixture.
Let's assume the mass of BaO in the original mixture is x grams, and the mass of CaO is y grams.
According to the given information, we have:
Mass of BaO (x) + Mass of CaO (y) = 1.5 g ----(1)
We are also given that the mass of the mixed sulfates is 3.0 g. The formula for the mixed sulfates is (BaSO4)z(CaSO4)w, where z and w are the respective moles of BaSO4 and CaSO4.
The molecular weight of BaSO4 is 233 g/mol, and the molecular weight of CaSO4 is 136 g/mol. Hence, we can write two equations based on the given information:
x/(137.33 g/mol) + y/(71.08 g/mol) = z/(233 g/mol) + w/(136 g/mol) ----(2) (Converting x and y to moles using their respective molecular weights)
x + y = z + w ----(3) (Since the number of moles is the same before and after the reaction)
We can rewrite equation (3) as:
x + y - z - w = 0 ----(4)
Now, let's solve equations (1), (2), and (4) simultaneously to find the values of x and y:
From equation (4), we have:
x + y - z - w = 0
x + y = z + w
x = z + w - y ----(5)
Substituting equation (5) into equation (2):
(z + w - y)/(137.33) + y/(71.08) = z/(233) + w/(136)
Simplifying the equation:
1.95z + 1.96w = 1.7y + 0.67z
1.28z + 0.96w = 1.7y ----(6)
We can rewrite equation (1) as:
x + y = 1.5
z + w - y + y = 1.5
z + w = 1.5 ----(7)
Solving equations (6) and (7):
1.28z + 0.96w = 1.7(1.5 - z - w)
1.28z + 0.96w = 2.55 - 1.7z - 1.7w
3.98z + 2.66w = 2.55 ----(8)
Now, we have two simultaneous equations (8) and (7). Solving these equations will give us the values of z and w, which represent the moles of BaSO4 and CaSO4, respectively.
After finding the values of z and w, we can calculate the percent of Ba and Ca in the original mixture using the following formulas:
Percent Ba = (z * 233 g/mol) / (z * 233 g/mol + w * 136 g/mol) * 100
Percent Ca = (w * 136 g/mol) / (z * 233 g/mol + w * 136 g/mol) * 100
Please note that solving equations (6) and (7) requires numerical methods, such as substitution or graphical methods, as they are non-linear equations.
To find the percent of Ba and Ca in the original mixture, we need to determine the masses of BaO and CaO that make up the mixture.
Let's assume that the mass of BaO in the mixture is x g. Therefore, the mass of CaO in the mixture would be (1.5 - x) g, as the total mass of the mixture is given as 1.5 g.
When these oxides are converted to their corresponding sulfates, the masses of the resulting mixed sulfates will be the same as the masses of the original oxides.
Given that the mass of the mixed sulfates is 3.0 g, we can set up the following equation:
Mass of BaSO4 + Mass of CaSO4 = 3.0 g
To calculate the percent Ba and Ca, we need to determine the masses of Ba and Ca in the mixed sulfates. The molar mass of BaSO4 is 233.4 g/mol, and the molar mass of CaSO4 is 136.2 g/mol.
Let's assume the mass of BaSO4 in the mixed sulfates is y g and the mass of CaSO4 is (3.0 - y) g.
Using the molar masses, we can convert the masses of BaSO4 and CaSO4 to moles:
Moles of BaSO4 = y g / 233.4 g/mol
Moles of CaSO4 = (3.0 - y) g / 136.2 g/mol
Since the stoichiometric ratio between BaSO4 and BaO is 1:1 (1 mole of BaSO4 corresponds to 1 mole of BaO) and the stoichiometric ratio between CaSO4 and CaO is also 1:1, the moles of BaO and CaO in the original mixture will be the same as the moles of BaSO4 and CaSO4 in the mixed sulfates.
Now, we can set up another equation to solve for y, the mass of BaSO4 in the mixed sulfates:
Moles of BaO = y g / 233.4 g/mol
Moles of CaO = (3.0 - y) g / 136.2 g/mol
Since the moles of BaO and CaO in the original mixture should add up to 1.5 g, we can write the following equation:
(y g / 233.4 g/mol) + ((3.0 - y) g / 136.2 g/mol) = 1.5 g
Now, we can solve this equation to find the value of y, which will give us the mass of BaSO4 in the mixed sulfates. Once we have y, we can find the mass of CaSO4 by subtracting y from 3.0 g.
Finally, we can calculate the percent Ba and Ca in the original mixture by dividing the masses of BaO and CaO by 1.5 g and multiplying by 100.
am = atoomic mass
mm = molar mass
Let X = mass BaO in the sample
and Y = mass CaO in the sample
So % Ba = [X*(am Ba/mm BaO)/1.5]*100 = ?
%Ca = [Y*(am Ca/mm CaO/1.5)]*100 = ?
The remainder of the problem is to determine the X and Y and you do that by setting up two equations and solving them simultaneously.
eqn1 is X + Y = 1.5 g
eqn2 is (mmBaSO4/mmBaO)X + (mmCaSO4/mmCaO)Y = 3.0 g
Solve eqn 1 and eqn2 simultaneously and plug X and Y into those % equations at top to obtain %Ba and %Ca.