4.72 g of a compound of carbon, hydrogen, and silver was burned in an atmosphere of oxygen, yielding 7.95 g of CO2, 1.02 g of H2O and 3.02 g of a mixture of silver and silver oxide. Because the production of this mixture yielded an indeterminate value for the amount of silver, another sample of the compound weighing 8.12 g was reacted with a solution of NaCl, yielding 5.57 g of AgCl. What is the empirical formula of the compound?
do the silver one first
Ag 108 g/mol
Cl 35.5 g/mol
AgCl = 143.5 g/mol
so 5.57 g AgCl has (108/143.5)5.57 = 4.19 g of Ag
so 8.12 g stuff has 4.19 g Ag
so 4.72 g stuff has 2.44 g Ag
so we have 4.72-2.44 = 2.28 g of C and H
we got 7.95 g of CO2
C = 12 g/mol
O2 = 32 g/mol
CO2 = 44 g/mol
12/44 *7.95 = 2.17 g C
we got 1.02 g of H2O
H2 = 2 g/mol
O = 16 g/mol
H2O = 18 g/mol
H2 = 2/18 * 1.02 = .113= g H2
so our compound had
2.17 g of C
.113 g of H2
2.44 g of Ag
good, that checks with total of 4.72
now chemistry
2.17/12 = .181 mol C
.113/2 =.0565 mol H2=.113 mol H
2.44/108 = .0226 mol Ag
5 H for every Ag .113/.0226
8 C for every Ag .181/.0226
so
C8 H5 Ag
To determine the empirical formula of the compound, we first need to calculate the number of moles of each element present.
1. Start by finding the number of moles of CO2:
- The molar mass of CO2 is 44.01 g/mol.
- Divide the mass of CO2 (7.95 g) by the molar mass to find the number of moles:
Moles of CO2 = 7.95 g / 44.01 g/mol = 0.1805 mol
2. Next, calculate the number of moles of H2O:
- The molar mass of H2O is 18.02 g/mol.
- Divide the mass of H2O (1.02 g) by the molar mass to find the number of moles:
Moles of H2O = 1.02 g / 18.02 g/mol = 0.0564 mol
3. Calculate the number of moles of Ag in the Ag/Ag2O mixture:
- The molar mass of Ag is 107.87 g/mol.
- Divide the mass of the Ag/Ag2O mixture (3.02 g) by the molar mass to find the number of moles of Ag:
Moles of Ag = 3.02 g / 107.87 g/mol = 0.028 mol
4. Calculate the number of moles of O in the Ag/Ag2O mixture:
- We know that the Ag/Ag2O mixture consists of both Ag and Ag2O, and the difference in mass (3.02 g - mass of Ag) corresponds to the mass of O.
- The molar mass of Ag2O is 231.74 g/mol, which means it contains (2 * 107.87 g/mol) + 16.00 g/mol = 231.74 g/mol.
- Calculate the mass of Ag in the Ag/Ag2O mixture:
Mass of Ag = Moles of Ag * Molar mass of Ag = 0.028 mol * 107.87 g/mol = 3.026 g
- Calculate the mass of O in the Ag/Ag2O mixture:
Mass of O = Mass of Ag/Ag2O mixture - Mass of Ag = 3.02 g - 3.026 g = -0.006 g (negative because it was consumed in the reaction)
Note: The negative value suggests that there was an error in the initial composition determination. Since the mass of Ag was determined to higher accuracy, it is usually safe to assume that the discrepancy is due to an experimental error in the determination of the mass of O in the Ag/Ag2O mixture.
5. Calculate the number of moles of AgCl:
- The molar mass of AgCl is (107.87 g/mol + 35.45 g/mol) = 143.32 g/mol.
- Divide the mass of AgCl (5.57 g) by the molar mass to find the number of moles:
Moles of AgCl = 5.57 g / 143.32 g/mol = 0.0388 mol
6. Calculate the number of moles of Ag from the AgCl:
- Since AgCl contains Ag, we can assume that the molar amount of AgCl equals the molar amount of Ag produced:
Moles of Ag = 0.0388 mol
7. Calculate the number of moles of C:
- Since the mass of Ag and O was determined to an indeterminate value, we can use the initial mass of the compound to determine the amount of C.
- Calculate the mass of C in the compound:
Mass of C = Initial mass of compound - mass of CO2 - mass of H2O - mass of Ag/Ag2O mixture
= 4.72 g - 7.95 g - 1.02 g - 3.02 g = -7.27 g (negative due to the experimental discrepancy)
Note: The negative value suggests errors in the initial mass measurement or in the mass determination of the other components. However, we can still determine the empirical formula of the compound by assuming the experimental errors mainly affected the mass measurements.
8. Calculate the number of moles of C using the above determined mass:
- The molar mass of C is 12.01 g/mol.
- Divide the mass of C (-7.27 g) by the molar mass to find the number of moles:
Moles of C = -7.27 g / 12.01 g/mol = -0.605 mol (negative due to the experimental discrepancy)
Now, we have determined the number of moles for each element in the compound. However, since the number of moles for Ag, O, and C resulted in negative values due to experimental discrepancies, we cannot determine the empirical formula of the compound with the given data.
To find the empirical formula of the compound, we need to determine the ratio of the different elements present in the compound.
Let's start by calculating the number of moles of each component:
1. CO2: molar mass of CO2 = (12.01 g/mol * 1) + (16.00 g/mol * 2) = 44.01 g/mol
Number of moles of CO2 = 7.95 g / 44.01 g/mol = 0.1807 mol
2. H2O: molar mass of H2O = (1.01 g/mol * 2) + (16.00 g/mol * 1) = 18.02 g/mol
Number of moles of H2O = 1.02 g / 18.02 g/mol = 0.0566 mol
3. Ag + Ag2O: To calculate the number of moles of Ag, we need to find the mass of Ag2O first.
Mass of Ag2O = Total mass of Ag + Ag2O - mass of AgCl
= 3.02 g - 5.57 g = -2.55 g (negative because mass of AgCl is greater than the total mass)
Number of moles of Ag2O = mass / molar mass = -2.55 g / (107.87 g/mol * 2) = 0.0118 mol (approximately)
Next, we need to find the ratios of carbon, hydrogen, and silver in the compound.
The ratio of carbon in CO2 is 1:1, so the compound contains 0.1807 mol of carbon.
The ratio of hydrogen in H2O is 2:1, so the compound contains twice the amount of hydrogen, which is 2 * 0.0566 mol = 0.1132 mol of hydrogen.
The ratio of silver in Ag is 1:1, so the compound contains the same amount of silver as the number of moles of AgCl, which is 0.0118 mol.
Now, we can divide the number of moles of each element by the smallest number of moles (which corresponds to silver) to find the simplest whole-number ratio.
Carbon: 0.1807 mol / 0.0118 mol ≈ 15.33 ≈ 15
Hydrogen: 0.1132 mol / 0.0118 mol ≈ 9.59 ≈ 10
Silver: 0.0118 mol / 0.0118 mol = 1
Therefore, the empirical formula of the compound is AgC15H10.