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.
Well, this sounds like a chemistry problem with a dash of mystery! Let me put on my clown glasses and sprinkle some humor on it.
To solve this mystery, we need to use a little math. Don't worry, I'll be the one doing the calculating. Let's dive in!
First, we need to find the initial moles of CO2 using the ideal gas law. But let me ask you, why did the chemist use CO2? Because it was the only one invited to the flask party! Talk about a gas that knows how to socialize.
The ideal gas law is PV = nRT, but we need to solve for n (moles of CO2). So, n = PV/RT. Plugging in the numbers:
n = (0.750 atm) x (1.50 L) / (0.0821 atm L/mol K) x (30.0 + 273.15 K)
n = 0.0426 mol
Now, here comes the reaction: BaO(s) + CO2(g) -> BaCO3(s)
Let's assume that x grams of BaO were present in the mixture. That means, 5.16 g - x grams of CaO were present.
After the reaction, the remaining pressure of CO2 is given, so we can use the ideal gas law again to find the moles of CO2:
n2 = (0.230 atm) x (1.50 L) / (0.0821 atm L/mol K) x (30.0 + 273.15 K)
n2 = 0.0169 mol
Since 1 mole of BaO forms 1 mole of BaCO3, and 1 mole of CaO forms 1 mole of CaCO3, the moles of CO2 reacted with BaO is n - n2, and the moles of CO2 reacted with CaO is n2:
moles of BaO = 0.0426 mol - 0.0169 mol
moles of CaO = 0.0169 mol
Now, my furry friend, let's calculate the mass percentages. The mass percent is the mass of an element divided by the total mass of the mixture, multiplied by 100. So:
mass percent of BaO = (mass of BaO / total mass) x 100
mass percent of BaO = (moles of BaO x molar mass of BaO / total mass) x 100
mass percent of BaO = (0.0257 mol x 137.33 g/mol / 5.16 g) x 100
And we're left with the suspense, isn't it exciting? Shall we solve it together?
To calculate the mass percentages of CaO(s) and BaO(s) in the mixture, we need to determine the moles of CaCO3(s) and BaCO3(s) formed.
Let's start by finding the moles of CO2(g) reacted:
P1V1 = n1RT
where P1 = initial pressure of CO2(g) = 750. torr
V1 = volume of the flask = 1.50 L
n1 = moles of CO2(g) initially
R = gas constant = 0.0821 L⋅atm/(K⋅mol)
T = temperature in Kelvin = (30.0 + 273) K
Plugging in the values:
n1 = (P1 * V1) / (R * T)
= (750. torr * 1.50 L) / (0.0821 L⋅atm/(K⋅mol) * 303 K)
Now, let's find the moles of CO2(g) remaining:
P2V2 = n2RT
where P2 = final pressure of CO2(g) = 230. torr
V2 = volume of the flask = 1.50 L
n2 = moles of CO2(g) remaining
R = gas constant = 0.0821 L⋅atm/(K⋅mol)
T = temperature in Kelvin = (30.0 + 273) K
Plugging in the values:
n2 = (P2 * V2) / (R * T)
= (230. torr * 1.50 L) / (0.0821 L⋅atm/(K⋅mol) * 303 K)
Next, we need to find the moles of CO2 reacted, which would be equal to the difference between the initial moles and the remaining moles:
moles of CO2 reacted = n1 - n2
Now, we can determine the moles of CaCO3(s) and BaCO3(s) formed. Since 1 mole of CO2 reacts with 1 mole of CaCO3 and 1 mole of BaCO3, the moles of CaCO3(s) and BaCO3(s) are equal to the moles of CO2 reacted.
moles of CaCO3(s) = moles of CO2 reacted
moles of BaCO3(s) = moles of CO2 reacted
To find the moles of CaO(s) and BaO(s), we use the balanced chemical equation that relates the formation of CaCO3(s) and BaCO3(s) to the initial amounts of CaO(s) and BaO(s):
CaO(s) + CO2(g) → CaCO3(s)
BaO(s) + CO2(g) → BaCO3(s)
Since the molar mass of CaCO3 is 100.09 g/mol and BaCO3 is 197.34 g/mol, we can use the moles of CaCO3(s) and BaCO3(s) to calculate the moles of CaO(s) and BaO(s).
moles of CaO(s) = moles of CaCO3(s) * (56.08 g/mol CaCO3) / (100.09 g/mol CaCO3)
moles of BaO(s) = moles of BaCO3(s) * (76.23 g/mol BaCO3) / (197.34 g/mol BaCO3)
Finally, we can determine the mass percentages:
mass percentage of CaO(s) = (mass of CaO(s) / total mass of mixture) * 100%
mass percentage of BaO(s) = (mass of BaO(s) / total mass of mixture) * 100%
Please note that we need to know the total mass of the mixture to calculate the mass percentages. Is the total mass of the mixture provided?
To calculate the mass percentages of CaO(s) and BaO(s) in the mixture, we can use stoichiometry and the ideal gas law.
Step 1: Calculate the number of moles of CO2(g) used in the reaction:
According to the ideal gas law, PV = nRT, where:
P = pressure in atm,
V = volume in liters,
n = number of moles,
R = ideal gas constant (0.0821 L·atm/mol·K), and
T = temperature in Kelvin.
Converting the given values:
Initial pressure (Pi) = 750 torr = 750/760 atm (assuming 1 atm = 760 torr)
Final pressure (Pf) = 230 torr = 230/760 atm
Temperature (T) = 30.0 + 273.15 K (converting Celsius to Kelvin)
Calculating the number of moles of CO2(g) used in the reaction:
n = (Pi * V) / (R * T)
= ((750/760) * 1.50) / (0.0821 * (30.0 + 273.15))
Step 2: Determine the mole ratios between CO2(g), CaO(s), and BaO(s) in the reaction:
The balanced chemical equation for the reaction between CO2(g), CaO(s), and BaO(s) is:
CaO(s) + CO2(g) -> CaCO3(s)
BaO(s) + CO2(g) -> BaCO3(s)
From the equation, we see that 1 mole of CO2 reacts with 1 mole of CaO and 1 mole of BaO. Therefore, the mole ratios are 1:1:1.
Step 3: Calculate the number of moles of CaO(s) and BaO(s) in the mixture:
Since the mole ratios are 1:1:1, the number of moles of CaO(s) and BaO(s) will be equal to the number of moles of CO2(g) used in the reaction.
Step 4: Calculate the mass of CaO(s) and BaO(s) in the mixture:
To calculate the mass, we can use the molar masses of CaO (56.08 g/mol) and BaO (153.33 g/mol).
Mass of CaO(s) = number of moles of CaO(s) * molar mass of CaO
Mass of BaO(s) = number of moles of BaO(s) * molar mass of BaO
Step 5: Calculate the mass percentages:
Mass percentage of CaO(s) = (Mass of CaO(s) / total mass of the mixture) * 100%
Mass percentage of BaO(s) = (Mass of BaO(s) / total mass of the mixture) * 100%
Now you can plug in the values obtained from the previous steps to get the final mass percentages.