metallocene are metals sandwiched by two cyclopentadienyl ions, (c5h5)–. a metallocene sample of unknown metal, mc5h5 (all 5 are subscripts) was burned in air. products of combustion found to contain 46.08488% carbon dioxide, 9.42644% water vapour and the rest are metal (i) oxide. all products are in mass percent. the mass ratio of stoichiometric amount of oxygen to the burned metallocene is 1:1.295. what is the name of the metal in the metallocene sample? prove by showing your complete solution
To find the name of the metal in the metallocene sample, we will need to analyze the given information and perform some calculations.
Let's assume the formula of the unknown metal, mc5h5, is M(C5H5)2.
1. Calculate the empirical formula of the combustion products:
a) Start with 100g of the sample.
b) The mass of carbon dioxide (CO2) produced is 46.08488g.
The molar mass of carbon dioxide = 12.01g/mol + 2*(16.00g/mol) = 44.01g/mol.
Convert grams to moles: 46.08488g / 44.01g/mol ≈ 1.0483 mol CO2.
Since there is one carbon in C5H5, the moles of carbon in CO2 is also 1.0483 mol.
Therefore, the empirical formula for carbon is C1.
c) The mass of water vapor (H2O) produced is 9.42644g.
The molar mass of water = 2*(1.01g/mol) + 16.00g/mol = 18.02g/mol.
Convert grams to moles: 9.42644g / 18.02g/mol ≈ 0.5228 mol H2O.
Since there are 10 hydrogens in C5H5, the moles of hydrogen in H2O are 10 * 0.5228 mol = 5.228 mol.
Therefore, the empirical formula for hydrogen is H5.
d) For metal oxide, we can assume its empirical formula is MOx.
The total mass of metal (M) in the sample is 100g - (46.08488g + 9.42644g) = 44.48868g.
The molar mass of metal is unknown, so we'll call it "x."
Convert grams to moles: 44.48868g / x(g/mol) = 1 mol M.
Therefore, the empirical formula for metal (M) is M1.
2. Calculate the ratio of elements in the empirical formula:
Carbon:Hydrogen:Metal = C1:H5:M1
3. Calculate the number of moles of oxygen required to combust the metallocene sample:
We know that the mass ratio of stoichiometric amount of oxygen to the burned metallocene is 1:1.295.
Let's assume the mass of oxygen required is "y."
The mass of the compound M(C5H5)2 is 100g.
The mass of oxygen in the compound is y(g).
So, (100g - y(g))/(y(g)) = 1.295.
Solving this equation for y gives y ≈ 35.118g.
4. Determine the empirical formula for oxygen:
The molar mass of oxygen is 16.00g/mol.
Convert grams to moles: 35.118g / 16.00g/mol ≈ 2.195 mol O2.
5. Determine the ratio of moles between elements in the empirical formula:
Carbon:Hydrogen:Metal:Oxygen = 1:5:1:(2.195/2.195) = 1:5:1:1
From the above ratios, we can deduce that the metal in the metallocene sample is iron (Fe). The empirical formula for the metallocene compound M(C5H5)2 is Fe(C5H5)2.
Please note that this is a step-by-step solution based on the given information and assumptions.
To determine the metal in the metallocene sample, we need to calculate the molar ratio of the elements present in the combustion products. From the given information, we know that the products of combustion are carbon dioxide (CO2), water vapor (H2O), and metal oxide (MO).
Let's assume the molecular weight of the metallocene is M, and the molecular weight of the metal oxide (MO) is A. We can now proceed with the calculations.
1. Calculate the mass of carbon dioxide (CO2):
Mass of CO2 = 46.08488% of total mass of products
2. Calculate the mass of water vapor (H2O):
Mass of H2O = 9.42644% of total mass of products
3. Calculate the mass of metal oxide (MO):
Mass of MO = Total mass of products - (Mass of CO2 + Mass of H2O)
4. Determine the moles of CO2:
Moles of CO2 = Mass of CO2 / Molar mass of CO2
5. Determine the moles of H2O:
Moles of H2O = Mass of H2O / Molar mass of H2O
6. Determine the moles of metal oxide (MO):
Moles of MO = Mass of MO / Molar mass of MO
7. Calculate the oxygen-to-metallocene ratio:
Oxygen-to-metallocene ratio = Moles of O2 / Moles of Metallocene
Moles of O2 = Moles of MO
8. Calculate the mass of oxygen (O2):
Mass of O2 = Oxygen-to-metallocene ratio * Molar mass of O2
9. Calculate the mass of metallocene (M):
Mass of Metallocene = Mass of O2 / Oxygen-to-metallocene ratio
Now, we can substitute the given mass ratio of stoichiometric amount of oxygen to the burned metallocene (1:1.295) and solve for the metal's molar mass.
10. Calculate the mass of O2 that combines with the metallocene:
Mass of O2 = 1.295 * Mass of Metallocene
11. Calculate the moles of O2 that combines with the metallocene:
Moles of O2 = Mass of O2 / Molar mass of O2
12. Calculate the moles of metallocene (M):
Moles of Metallocene = Moles of O2
13. Calculate the molar mass of the metal (A):
Molar mass of Metal (A) = Mass of Metallocene / Moles of Metallocene
Now that we have obtained the molar mass of the metal (A), we can determine its atomic number, which will identify the metal.
14. Determine the metal's atomic number using the molar mass:
Consult a periodic table or online resource to identify the metal with the specified molar mass (A).
By following these steps and performing the calculations, you can determine the name of the metal in the metallocene sample.