Iron forms a series of compounds of the type Fex(CO)y. If you heat any of these compounds in air , they decompose to Fe2O3 and CO2 gas. After heating a 0.142g sample of Fe(CO)y, You isolate the CO2 in a 1.50 L flask at 25 Degrees celsius. The pressure is 44.9 mmHg. What is the formula of Fex(CO)y?
Well, let's analyze the problem step-by-step. From the information provided, we know that when you heat the compound Fe(CO)y in air, it decomposes to form Fe2O3 and CO2 gas. After heating a sample, you isolate the CO2 in a flask.
To find the formula of Fex(CO)y, we need to calculate the number of moles of CO2 produced. We can then use this information to determine the ratio of Fe to CO in the compound.
Given:
Mass of Fe(CO)y = 0.142g
Volume of flask = 1.50 L
Pressure in flask = 44.9 mmHg
Temperature = 25°C
First, let's convert the pressure to atm:
1 atm = 760 mmHg.
So, the pressure in atm is 44.9 mmHg / 760 mmHg = 0.0590 atm.
Now, we can use the ideal gas law to find the number of moles of CO2:
PV = nRT
Where:
P = pressure in atm
V = volume in L
n = number of moles
R = ideal gas constant (0.0821 L*atm/mol*K)
T = temperature in Kelvin
Convert temperature from Celsius to Kelvin:
T = 25°C + 273.15 = 298.15 K
Rearranging the ideal gas law equation to solve for n:
n = PV / RT
Plugging in the values:
n = (0.0590 atm) * (1.50 L) / (0.0821 L*atm/mol*K * 298.15 K)
n = 0.0023 mol
We know that each mole of Fe(CO)y produces one mole of CO2 upon decomposition.
Since we have 0.0023 mol of CO2, we can conclude that we had 0.0023 mol of Fe(CO)y initially.
To find the ratio of Fe to CO in the compound, we divide the number of moles of Fe by the number of moles of CO:
Fe : CO = 0.0023 mol : 0.0023 mol
This simplifies to 1 : 1.
Therefore, the formula of Fex(CO)y is Fe(CO). Each molecule of Fe(CO)y contains one iron (Fe) atom and one carbon monoxide (CO) molecule.
I hope this explanation didn't make you feel "iron deficient" in humor!
To determine the formula of Fex(CO)y, we need to calculate the number of moles of CO2 produced and use it to find the stoichiometric ratio of Fe to CO in the compound.
Step 1: Calculate the number of moles of CO2:
To do this, we can use the ideal gas law equation: PV = nRT.
Given:
Volume (V) = 1.50 L
Pressure (P) = 44.9 mmHg (which needs to be converted to atm)
Temperature (T) = 25 degrees Celsius (which needs to be converted to Kelvin)
First, let's convert pressure from mmHg to atm:
1 atm = 760 mmHg
44.9 mmHg = 44.9/760 = 0.059 atm
Next, let's convert temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 25 + 273.15 = 298.15 K
Now we can substitute the values into the ideal gas law equation: PV = nRT
(0.059 atm)(1.50 L) = n(0.0821 L·atm/(mol·K))(298.15 K)
Solving for n:
n = (0.059 atm * 1.50 L) / (0.0821 L·atm/(mol·K) * 298.15 K)
n ≈ 0.032 mol
Step 2: Calculate the stoichiometric ratio of Fe to CO:
Since the compound is Fex(CO)y, the ratio of Fe to CO can be represented as x: y.
From the given information, we know that 0.142g of Fe(CO)y decomposes to produce 0.032 mol of CO2.
Molar mass of CO2 = 12.01 g/mol (C) + 2 * 16.00 g/mol (O) = 44.01 g/mol
Using the molar mass of CO2, we can calculate the moles of CO2 from the mass of CO2:
moles of CO2 = mass of CO2 / molar mass of CO2
moles of CO2 = 0.032 mol
Since the mole ratio between CO2 and Fe(CO)y is 1:1, this means 0.032 mol of CO2 is produced from 0.032 mol of Fe(CO)y.
The molar mass of Fe(CO)y can be calculated using the mass of Fe(CO)y and the number of moles of Fe(CO)y:
mass of Fe(CO)y = 0.142g
moles of Fe(CO)y = mass of Fe(CO)y / molar mass of Fe(CO)y
By rearranging the equation:
molar mass of Fe(CO)y = mass of Fe(CO)y / (moles of Fe(CO)y / moles of CO2)
molar mass of Fe(CO)y = 0.142g / (0.032 mol / 0.032 mol)
molar mass of Fe(CO)y = 0.142g
The molar mass of Fe(CO)y is approximately equal to the mass of Fe(CO)y, which suggests that the compound is mononuclear.
Therefore, the formula for Fex(CO)y is Fe(CO)3.
To determine the formula of Fex(CO)y, we need to use the given information about the decomposition of the compound and the properties of CO2 gas.
First, let's calculate the number of moles of CO2 present in the 1.50 L flask at 25 degrees Celsius and 44.9 mmHg pressure using the ideal gas law equation:
PV = nRT
Where:
P = pressure in atm (convert mmHg to atm by dividing by 760: 44.9 mmHg / 760 mmHg/atm = 0.0591 atm)
V = volume in liters (1.50 L)
n = number of moles (unknown)
R = ideal gas constant (0.0821 L * atm / (mol * K))
T = temperature in Kelvin (convert Celsius to Kelvin: 25 °C + 273.15 = 298.15 K)
Plugging in the values into the ideal gas law equation:
0.0591 atm * 1.50 L = n * 0.0821 L * atm / (mol * K) * 298.15 K
n = (0.0591 atm * 1.50 L) / (0.0821 L * atm / (mol * K) * 298.15 K)
n = 0.003003 mol
Next, we need to determine the number of moles of Fe(CO)y that decomposed to produce the 0.003003 mol of CO2. To do this, we need to find the molar mass of Fe(CO)y.
The molar mass of CO2 is: 12.01 g/mol + 2 * 16.00 g/mol = 44.01 g/mol.
The number of moles of CO2 produced is equal to the number of moles of Fe(CO)y that decomposed, since the reaction is 1:1. Therefore, we can calculate the mass of Fe(CO)y using the following equation:
mass = moles * molar mass
mass = 0.003003 mol * 44.01 g/mol
mass = 0.1322 g
However, we are given that the initial mass of the Fe(CO)y sample is 0.142 g. By subtracting the mass of CO2 produced from the initial mass, we can find the mass of iron:
mass of iron = initial mass - mass of CO2
mass of iron = 0.142 g - 0.1322 g
mass of iron = 0.0098 g
Now, we need to find the ratio of iron to carbon monoxide in the compound Fe(CO)y. We can do this by comparing the number of moles of iron to the number of moles of CO.
The molar mass of iron (Fe) is 55.85 g/mol.
moles of iron = mass of iron / molar mass of iron
moles of iron = 0.0098 g / 55.85 g/mol
moles of iron = 0.00018 mol
Since the reaction is 1:1, the moles of iron is also equal to the moles of CO (y is assumed to be 1 in this case).
Finally, we can determine the formula of Fex(CO)y. Since the moles of iron and CO are equal (0.00018 mol) and y is assumed to be 1, the formula can be written as:
Fe(CO)
Therefore, the formula of the compound is Fe(CO).