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When it comes to chemical reactions, the concept of the limiting reactant is crucial. This is because it determines the maximum amount of product that can be formed. The limiting reactant is the substance that is completely consumed when the reaction goes to completion. In our example, we have iron (Fe) and carbon monoxide (CO) reacting to form iron carbonyl. To find out which reactant is limiting, we must first calculate the amount of each reactant available and see which one runs out first. This involves comparing the mole ratios. For our reaction, 1 mole of iron requires 5 moles of carbon monoxide to complete the reaction as per the equation: Fe + 5 CO → Fe(CO)₅. In the given problem, the moles of iron are 0.063, which would require 0.315 moles of CO. However, we only have 0.218 moles of CO available, making carbon monoxide the limiting reactant. Since there is not enough CO to convert all of the available iron into product, CO limits the reaction and thus determines the theoretical yield of iron carbonyl.

The ideal gas law is an essential tool for connecting the physical properties of gases: pressure (P), volume (V), and temperature (T) with the amount of gas in moles (n). It is expressed as:\(PV = nRT\).In this equation, \(R\) is the ideal gas constant, which equals 0.0821 L atm/mol K. To solve for the number of moles in a gas sample, rearrange the equation to: \(n = \frac{PV}{RT}\).Let's apply this to find the moles of CO in our reaction. We start by converting the pressure from mm Hg to atm, as calculations using the ideal gas law require standard units.1 atm = 760 mm Hg, so \(732 \text{ mm Hg} = 0.963 \text{ atm}\).Also, the temperature needs to be in Kelvin:\(T(\text{K}) = 23 + 273.15 = 296.15 \text{ K}\).Now we can find the moles of CO:\(n = \frac{(0.963 \text{ atm})(5.50 \text{ L})}{(0.0821 \text{ L atm/mol K})(296.15 \text{ K})} \approx 0.218 \text{ mole CO}\).This calculation correctly shows that the amount of CO available for the reaction is 0.218 moles, another hint towards identifying the limiting reactant.

To understand productivity in chemical reactions, knowing how to calculate molar mass is essential. Molar mass, often measured in grams per mole, is important for converting between the mass of a substance and its moles.To calculate it:- Add up the atomic masses of all elements in the compound (using the periodic table for atomic masses).For instance, iron carbonyl \(\text{Fe(CO)}_5\) requires knowledge of atomic masses of iron and carbon monoxide. The molar mass of iron is 55.85 g/mol, and carbon (12.01 g/mol) plus oxygen (16.00 g/mol) gives CO a molar mass of 28.01 g/mol. Therefore, for \(\text{Fe(CO)}_5\):- Calculate as: \(55.85 \text{ g/mol for Fe} + 5 \times 28.01 \text{ g/mol for CO} = 195.9 \text{ g/mol}\).This molar mass helps determine both the moles of \(\text{Fe(CO)}_5\) possible from limiting CO and ultimately compute the theoretical yield (i.e., predicted mass of product resulting from a complete reaction of limiting reactant). In our example case, with 0.0436 moles of \(\text{Fe(CO)}_5\) produced and a molar mass of 195.9 g/mol, the theoretical yield is 8.54 grams.