Fe2O3 + 3CO --> 2Fe + 3CO2
a 16.2 L sample of CO at 1.5 atm and 200 C is combind with 15.39 g Fe2O3.
how many moles of CO are available for the reaction?
what is the limiting reacta?
How many moles of Fe are formed?
1. Convert 16.2 L CO to moles using PV = nRT.
2. Convert 15.39 g Fe2O3 to moles. Moles = gram/molar mass.
3a. Using the coefficients in the balanced equation, convert moles CO to moles Fe.
3b. Use same procedue to convert moles Fe2O3 to moles Fe.
3c. It is likely that moles from 3a and 3b will be different. Obviously, one must be incorrect. The correct one in limiting reagent problems is ALWAYS the smaller value and the reactant producing that value is the limiting reagent.
4. The problem doesn't ask for it but you could then use the smaller value and convert to grams Fe. grams = moles x molar mass.
To find the number of moles of CO available for the reaction, we can use the ideal gas law equation:
PV = nRT
Given:
P = 1.5 atm
V = 16.2 L
T = 200 °C = (200 + 273) K
R = 0.0821 L·atm/(K·mol)
Converting temperature to Kelvin:
T = 200 + 273 = 473 K
Rearranging the equation to solve for moles:
n = PV / RT
Substituting the given values:
n = (1.5 atm) * (16.2 L) / (0.0821 L·atm/(K·mol) * 473 K)
n = 1.5 * 16.2 / (0.0821 * 473)
Calculating the value of n:
n = 3.812 moles
Therefore, there are 3.812 moles of CO available for the reaction.
To determine the limiting reactant, we need to compare the number of moles of CO available with the stoichiometric ratio of Fe2O3 and CO.
Looking at the balanced equation:
Fe2O3 + 3CO -> 2Fe + 3CO2
The stoichiometric ratio between Fe2O3 and CO is 1:3. So, for every 3 moles of CO, 1 mole of Fe2O3 is required.
From the previous calculation, we found that there are 3.812 moles of CO available.
To find the amount of Fe2O3 required for this many moles of CO, we use the stoichiometric ratio:
(3 moles CO) x (1 mole Fe2O3 / 3 moles CO) = 1 mole Fe2O3
Therefore, we require 1 mole of Fe2O3 for the given number of moles of CO.
Since we have only 15.39 g Fe2O3 available, which is less than 1 mole, Fe2O3 is the limiting reactant.
To calculate the number of moles of Fe formed, we use the stoichiometric ratio between Fe2O3 and Fe:
Fe2O3 + 3CO -> 2Fe + 3CO2
The stoichiometric ratio between Fe2O3 and Fe is 1:2. So, for every 1 mole of Fe2O3, we get 2 moles of Fe.
Since Fe2O3 is the limiting reactant, we have 1 mole of Fe2O3 reacting, which results in 2 moles of Fe being formed.
Therefore, 2 moles of Fe are formed in the reaction.
To determine the number of moles of CO available for the reaction, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure in atm
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 atm L/mol K)
T = temperature in Kelvin
We need to convert the temperature from Celsius to Kelvin before using the equation. Adding 273.15 to 200°C gives us 473.15 K.
Plugging in the given values:
P = 1.5 atm
V = 16.2 L
R = 0.0821 atm L/mol K
T = 473.15 K
We can rearrange the equation to solve for moles (n):
n = PV / RT
n = (1.5 atm * 16.2 L) / (0.0821 atm L/mol K * 473.15 K)
n ≈ 0.496 moles
Therefore, approximately 0.496 moles of CO are available for the reaction.
To determine the limiting reactant, we need to compare the moles of CO available with the moles of Fe2O3. From the balanced equation, we can see that the stoichiometric ratio between CO and Fe2O3 is 3:1.
Given:
Mass of Fe2O3 = 15.39 g
Molar mass of Fe2O3 = 159.69 g/mol (Fe2O3 has 2 iron atoms with a molar mass of 55.85 g/mol each, plus 3 oxygen atoms with a molar mass of 16 g/mol each)
To find the number of moles of Fe2O3:
n = mass / molar mass
n = 15.39 g / 159.69 g/mol
n ≈ 0.0964 moles
Since the stoichiometric ratio is 3:1, we need three times the number of moles of CO compared to Fe2O3 for the reaction to proceed completely. However, we only have 0.496 moles of CO available, which is greater than 0.0964 moles of Fe2O3.
Therefore, Fe2O3 is the limiting reactant.
Using the stoichiometric ratio from the balanced equation, we know that for every 3 moles of CO, we get 2 moles of Fe.
From the given information, we have:
Number of moles of CO = 0.496 moles
Using the stoichiometric ratio:
Number of moles of Fe = (2/3) * (0.496 moles)
Number of moles of Fe ≈ 0.331 moles
Therefore, approximately 0.331 moles of Fe are formed.