Question

iron ore is reduced to pure iron by smelting, during which the iron (iii) oxide reacts with carbon monoxide gas, like this:
fe₂o₃(s)+3co(g)→2fe(s)+3co₂(g)
suppose an engineer decides to study the rate of this reaction. he prepares four reaction vessels with 142.6 g of solid iron (iii) oxide and 5.00 g of carbon monoxide gas each. the volume and temperature of each vessel is shown in the table below.
arrange the reaction vessels in decreasing order of initial rate of reaction. in other words, select a \1\ next to the vessel in which the engineer can reasonably expect the initial rate of reaction to be highest, a \2\ next to the vessel in which the initial rate of reaction would be next highest, and so on.

Explanation:

Step1: Calculate the concentration of CO

The amount of CO is \(n = \frac{m}{M}\), where \(M(CO)=28g/mol\), \(m = 5.00g\), so \(n=\frac{5.00g}{28g/mol}\approx0.179mol\).
The concentration \(c=\frac{n}{V}\).
For vessel A: \(V = 2.0L\), \(c_A=\frac{0.179mol}{2.0L}=0.0895mol/L\).
For vessel B: \(V = 8.0L\), \(c_B=\frac{0.179mol}{8.0L}=0.0224mol/L\).
For vessel C: \(V = 4.0L\), \(c_C=\frac{0.179mol}{4.0L}=0.0448mol/L\).
For vessel D: \(V = 1.0L\), \(c_D=\frac{0.179mol}{1.0L}=0.179mol/L\).

Step2: Analyze the effect of concentration on reaction rate

According to the rate - law (assuming the reaction is of a certain order with respect to CO, and since temperature is the same for all vessels (\(T = 1000^{\circ}C\)), and for a reaction \(aA + bB
ightarrow\) products, rate \(r = k[A]^m[B]^n\) (here assume the rate is mainly related to CO as other reactants (Fe₂O₃ is solid, its concentration is constant)). When \(m>0\) (common reaction order), rate is proportional to the concentration of CO.
Since \(c_D>c_A>c_C>c_B\)

Answer:

D (1), A (2), C (3), B (4)