A chemist weighed out 5.16 g of a mixture containing unknown amunts of BaO(s) and CaO(s) and placed the sample in a 1.50-L flask containing CO2(g) at 30.0°C and 750. torr. After the reaction to form BaCO3(s) and CaCO3(s) was completed, the pressure of CO2(g) remaining was 230. torr. Calculate the mass percentages of CaO(s) and BaO(s) in the mixture.
To calculate the mass percentages of CaO(s) and BaO(s) in the mixture, we need to use the ideal gas law and stoichiometry.
First, let's determine the number of moles of CO2 present before and after the reaction using the ideal gas law equation:
PV = nRT
Where:
P = Pressure of CO2(g)
V = Volume of the flask
n = Number of moles
R = Ideal gas constant
T = Temperature in Kelvin
Given data:
P(before) = 750. torr = 750. mmHg (since 1 atm = 760 mmHg)
P(after) = 230. torr = 230. mmHg
V = 1.50 L
T = 30.0°C = 273.15 + 30.0 = 303.15 K
Converting the pressures to atm:
P(before) = 750/760 = 0.987 atm
P(after) = 230/760 = 0.303 atm
Using the ideal gas law equation, we can calculate the number of moles of CO2 before and after the reaction:
n(before) = (P(before) * V) / (R * T)
n(after) = (P(after) * V) / (R * T)
Substituting the values:
n(before) = (0.987 atm * 1.50 L) / (0.0821 L·atm/(mol·K) * 303.15 K)
n(after) = (0.303 atm * 1.50 L) / (0.0821 L·atm/(mol·K) * 303.15 K)
Calculating the moles using these equations will give us the total number of moles of CO2 before and after the reaction.
Next, let's determine the moles of CO2 used in the reaction. Since the chemical equation for the reaction is:
BaO(s) + CO2(g) → BaCO3(s)
We know that the stoichiometric ratio between BaO(s) and CO2(g) is 1:1. Therefore, the number of moles of BaO(s) reacted is equal to the number of moles of CO2 reacted.
n(BaO reacted) = n(CO2 reacted)
To find the moles of BaO reacted, we can use the difference between the moles of CO2 before and after the reaction:
n(BaO reacted) = n(before) - n(after)
Now we can determine the moles of BaO and CaO in the mixture. Since both BaO and CaO react with the same number of moles of CO2, we can use the stoichiometric ratio between BaO and CaO given in the balanced chemical equation to relate their moles:
BaO(s) + CO2(g) → BaCO3(s) ... Stoichiometric ratio: 1:1
CaO(s) + CO2(g) → CaCO3(s) ... Stoichiometric ratio: 1:1
Let's assume the number of moles of CaO in the mixture is n(CaO), and the number of moles of BaO in the mixture is n(BaO).
n(BaO reacted) = n(CaO reacted)
Using this information, we can create two equations:
n(BaO reacted) = n(BaO)
n(CaO reacted) = n(CaO)
Solving these equations will give us the moles of BaO and CaO in the mixture.
Finally, to calculate the mass percentages of CaO and BaO in the mixture, we need to divide the mass of each compound by the total mass of the mixture and multiply by 100:
Mass percentage of CaO = (mass of CaO / total mass of mixture) * 100
Mass percentage of BaO = (mass of BaO / total mass of mixture) * 100
Now that we have the general steps to solve the problem, you can plug in the given values and perform the calculations to find the mass percentages of CaO and BaO in the mixture.